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Terwilliger, Paul M.

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Author ID: terwilliger.paul-m Recent zbMATH articles by "Terwilliger, Paul M."
Published as: Terwilliger, Paul; Terwilliger, Paul M.; Terwilliger, P.
Documents Indexed: 136 Publications since 1982
Co-Authors: 25 Co-Authors with 73 Joint Publications
558 Co-Co-Authors

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128 Publications have been cited 2,915 times in 630 Documents Cited by Year
The subconstituent algebra of an association scheme. I. Zbl 0785.05089
Terwilliger, Paul
195
1992
Two linear transformations each tridiagonal with respect to an eigenbasis of the other. Zbl 0980.05054
Terwilliger, Paul
159
2001
The subconstituent algebra of an association scheme. III. Zbl 0785.05091
Terwilliger, Paul
121
1993
Some algebra related to \(P\)- and \(Q\)-polynomial association schemes. Zbl 0995.05148
Ito, Tatsuro; Tanabe, Kenichiro; Terwilliger, Paul
109
2001
Leonard pairs and the Askey-Wilson relations. Zbl 1062.33018
Terwilliger, Paul; Vidunas, Raimundas
92
2004
Two relations that generalize the \(q\)-Serre relations and the Dolan-Grady relations. Zbl 1061.16033
Terwilliger, Paul
91
2001
Two linear transformations each tridiagonal with respect to an eigenbasis of the other; comments on the parameter array. Zbl 1063.05138
Terwilliger, Paul
77
2005
The subconstituent algebra of an association scheme. II. Zbl 0785.05090
Terwilliger, Paul
74
1993
Leonard pairs and the \(q\)-Racah polynomials. Zbl 1075.05090
Terwilliger, Paul
69
2004
An algebraic approach to the Askey scheme of orthogonal polynomials. Zbl 1102.33011
Terwilliger, Paul
69
2006
Tridiagonal pairs and the quantum affine algebra \(U_q(\widehat{\text{sl}}_2)\). Zbl 1128.16028
Ito, Tatsuro; Terwilliger, Paul
64
2007
Leonard pairs from 24 points of view. Zbl 1040.05030
Terwilliger, Paul
61
2002
Introduction to Leonard pairs. Zbl 1035.05103
Terwilliger, Paul
59
2003
Two linear transformations each tridiagonal with respect to an eigenbasis of the other; the TD-D canonical form and the LB-UB canonical form. Zbl 1079.15005
Terwilliger, Paul
51
2005
The quantum algebra \(U_q(\mathfrak{sl}_2)\) and its equitable presentation. Zbl 1090.17004
Ito, Tatsuro; Terwilliger, Paul; Weng, Chih-Wen
51
2006
The shape of a tridiagonal pair. Zbl 1037.17013
Ito, Tatsuro; Terwilliger, Paul
46
2004
The \(q\)-tetrahedron algebra and its finite dimensional irreducible modules. Zbl 1133.17011
Ito, Tatsuro; Terwilliger, Paul
44
2007
The tetrahedron algebra, the Onsager algebra, and the \(\mathfrak{sl}_2\) loop algebra. Zbl 1163.17026
Hartwig, Brian; Terwilliger, Paul
44
2007
Two non-nilpotent linear transformations that satisfy the cubic \(q\)-Serre relations. Zbl 1179.17017
Ito, Tatsuro; Terwilliger, Paul
44
2007
Tight distance-regular graphs. Zbl 0959.05121
Jurišić, Aleksandar; Koolen, Jack; Terwilliger, Paul
43
2000
The universal Askey-Wilson algebra. Zbl 1244.33015
Terwilliger, Paul
43
2011
The augmented tridiagonal algebra. Zbl 1236.17022
Ito, Tatsuro; Terwilliger, Paul
40
2010
A new inequality for distance-regular graphs. Zbl 0814.05074
Terwilliger, Paul
38
1995
Linear transformations that are tridiagonal with respect to both eigenbases of a Leonard pair. Zbl 1119.05111
Nomura, Kazumasa; Terwilliger, Paul
38
2007
Two linear transformations each tridiagonal with respect to an eigenbasis of the other: comments on the split decomposition. Zbl 1069.15005
Terwilliger, Paul
33
2005
The equitable presentation for the quantum group associated with a symmetrizable Kac-Moody algebra. Zbl 1106.17021
Terwilliger, Paul
32
2006
Finite-dimensional irreducible modules for the three-point \(\mathfrak{sl}_2\) loop algebra. Zbl 1207.17030
Ito, Tatsuro; Terwilliger, Paul
30
2008
Tridiagonal pairs of \(q\)-Racah type. Zbl 1177.33021
Ito, Tatsuro; Terwilliger, Paul
29
2009
Tight distance-regular graphs and the subconstituent algebra. Zbl 1014.05070
Go, Junie T.; Terwilliger, Paul
29
2002
The universal Askey-Wilson algebra and DAHA of type \((C_{1}^{\vee },C_{1})\). Zbl 1293.33022
Terwilliger, Paul
26
2013
The universal Askey-Wilson algebra and the equitable presentation of \(U_{q}(sl_{2})\). Zbl 1244.33016
Terwilliger, Paul
26
2011
A characterization of \(P\)- and \(Q\)-polynomial association schemes. Zbl 0663.05016
Terwilliger, Paul
24
1987
Distance-regular graphs and the \(q\)-tetrahedron algebra. Zbl 1193.17008
Ito, Tatsuro; Terwilliger, Paul
24
2009
Affine transformations of a Leonard pair. Zbl 1143.05337
Nomura, Kazumasa; Terwilliger, Paul
23
2007
A note on thin \(P\)-polynomial and dual-thin \(Q\)-polynomial symmetric association schemes. Zbl 0898.05084
Dickie, Garth A.; Terwilliger, Paul M.
22
1998
A new feasibility condition for distance-regular graphs. Zbl 0606.05045
Terwilliger, Paul
21
1986
The incidence algebra of a uniform poset. Zbl 0737.05032
Terwilliger, Paul
21
1990
The universal central extension of the three-point \(\mathfrak{sl}_2\) loop algebra. Zbl 1153.17008
Benkart, Georgia; Terwilliger, Paul
21
2007
Irreducible modules for the quantum affine algebra \(U_{q}(\mathfrak {\widehat{sl}_2})\) and its Borel subalgebra. Zbl 1106.17014
Benkart, Georgia; Terwilliger, Paul
20
2004
\(p\)-inverting pairs of linear transformations and the \(q\)-tetrahedron algebra. Zbl 1146.17009
Ito, Tatsuro; Terwilliger, Paul
20
2007
Tridiagonal pairs of Krawtchouk type. Zbl 1132.15010
Ito, Tatsuro; Terwilliger, Paul
20
2007
A classification of sharp tridiagonal pairs. Zbl 1225.15015
Ito, Tatsuro; Nomura, Kazumasa; Terwilliger, Paul
20
2011
Sharp tridiagonal pairs. Zbl 1193.05164
Nomura, Kazumasa; Terwilliger, Paul
20
2008
The structure of a tridiagonal pair. Zbl 1144.05331
Nomura, Kazumasa; Terwilliger, Paul
20
2008
Distance-regular graphs and (s,c,a,k)-graphs. Zbl 0511.05052
Terwilliger, Paul
20
1983
Balanced Leonard pairs. Zbl 1119.05110
Nomura, Kazumasa; Terwilliger, Paul
20
2007
Some trace formulae involving the split sequences of a Leonard pair. Zbl 1085.05070
Nomura, Kazumasa; Terwilliger, Paul
20
2006
Kite-free distance-regular graphs. Zbl 0829.05059
Terwilliger, Paul
19
1995
An introduction to Leonard pairs and Leonard systems. Zbl 0957.15500
Terwilliger, Paul
19
1999
Matrix units associated with the split basis of a Leonard pair. Zbl 1107.05103
Nomura, Kazumasa; Terwilliger, Paul
19
2006
Root systems and the Johnson and Hamming graphs. Zbl 0614.05048
Terwilliger, Paul
18
1987
The equitable basis for \({\mathfrak{sl}_2}\). Zbl 1277.17013
Benkart, Georgia; Terwilliger, Paul
18
2011
Distance-regular graphs with girth 3 or 4: I. Zbl 0588.05039
Terwilliger, Paul
18
1985
Eigenvalue multiplicities of highly symmetric graphs. Zbl 0495.05045
Terwilliger, Paul
17
1982
The Terwilliger algebra of an almost-bipartite \(P\)- and \(Q\)-polynomial association scheme. Zbl 1063.05135
Caughman, John S.; Maclean, Mark S.; Terwilliger, Paul M.
17
2005
The displacement and split decompositions for a \(Q\)-polynomial distance-regular graph. Zbl 1065.05097
Terwilliger, Paul
17
2005
The split decomposition of a tridiagonal pair. Zbl 1127.05108
Nomura, Kazumasa; Terwilliger, Paul
17
2007
The switching element for a Leonard pair. Zbl 1134.05105
Nomura, Kazumasa; Terwilliger, Paul
16
2008
Evaluation modules for the \(q\)-tetrahedron algebra. Zbl 1294.17014
Ito, Tatsuro; Rosengren, Hjalmar; Terwilliger, Paul
16
2014
Finite-dimensional irreducible \(U_q(\mathfrak{sl}_2)\)-modules from the equitable point of view. Zbl 1354.17012
Terwilliger, Paul
15
2013
Double affine Hecke algebras of rank 1 and the \(\mathbb Z_3\)-symmetric Askey-Wilson relations. Zbl 1220.33018
Ito, Tatsuro; Terwilliger, Paul
15
2010
Towards a classification of the tridiagonal pairs. Zbl 1193.05165
Nomura, Kazumasa; Terwilliger, Paul
15
2008
The determinant of \(AA^{*} - A^{*}A\) for a Leonard pair \(A,A^{*}\). Zbl 1108.15007
Nomura, Kazumasa; Terwilliger, Paul
15
2006
The Johnson graph \(J(d,r)\) is unique if \((d,r)\neq (2,8)\). Zbl 0587.05038
Terwilliger, Paul
15
1986
The Lusztig automorphism of the \(q\)-Onsager algebra. Zbl 1464.17022
Terwilliger, Paul
13
2018
The \(q\)-Onsager algebra and the positive part of \(U_q(\hat{\mathfrak{sl}}_2)\). Zbl 1386.17018
Terwilliger, Paul
13
2017
The \(q\)-Onsager algebra and the universal Askey-Wilson algebra. Zbl 1390.33038
Terwilliger, Paul
13
2018
Balanced sets and Q-polynomial association schemes. Zbl 0644.05016
Terwilliger, Paul
12
1988
Krawtchouk polynomials, the Lie algebra \(\mathfrak{sl}_2\), and Leonard pairs. Zbl 1261.33001
Nomura, Kazumasa; Terwilliger, Paul
12
2012
The subconstituent algebra of a distance-regular graph; thin modules with endpoint one. Zbl 1011.05066
Terwilliger, Paul
11
2002
The Rahman polynomials and the Lie algebra \(\mathfrak{sl}_{3}(\mathbb{C})\). Zbl 1353.33007
Iliev, Plamen; Terwilliger, Paul
11
2012
The classification of finite connected hypermetric spaces. Zbl 0618.05043
Terwilliger, Paul; Deza, Michel
10
1987
Distance-regular graphs of \(q\)-Racah type and the \(q\)-tetrahedron algebra. Zbl 1206.05103
Ito, Tatsuro; Terwilliger, Paul
10
2009
Distance-regular graphs of \(q\)-Racah type and the universal Askey-Wilson algebra. Zbl 1295.05100
Terwilliger, Paul; Žitnik, Arjana
10
2014
Taut distance-regular graphs and the subconstituent algebra. Zbl 1100.05104
MacLean, Mark S.; Terwilliger, Paul
10
2006
Dual bipartite Q-polynomial distance-regular graphs. Zbl 0921.05064
Dickie, Garth A.; Terwilliger, Paul M.
9
1996
The algebra \(U_q(\mathfrak{sl}_2)\) in disguise. Zbl 1348.17011
Bockting-Conrad, Sarah; Terwilliger, Paul
9
2014
The Drinfel’d polynomial of a tridiagonal pair. Zbl 1271.15003
Ito, Tatsuro; Terwilliger, Paul
9
2009
An inequality involving the local eigenvalues of a distance-regular graph. Zbl 1047.05045
Terwilliger, Paul
8
2004
P and Q polynomial schemes with \(q=-1\). Zbl 0675.05016
Terwilliger, Paul
8
1987
The subconstituent algebra of a bipartite distance-regular graph; thin modules with endpoint two. Zbl 1136.05076
MacLean, Mark S.; Terwilliger, Paul
8
2008
Tridiagonal pairs and the \(\mu \)-conjecture. Zbl 1155.15011
Nomura, Kazumasa; Terwilliger, Paul
8
2009
The diameter of bipartite distance-regular graphs. Zbl 0487.05038
Terwilliger, Paul
8
1982
Distance-regular graphs, pseudo primitive idempotents, and the Terwilliger algebra. Zbl 1035.05104
Terwilliger, Paul; Weng, Chih-wen
8
2004
Bipartite \(Q\)-polynomial distance-regular graphs and uniform posets. Zbl 1271.05105
Miklavič, Štefko; Terwilliger, Paul
7
2013
Tridiagonal pairs of \(q\)-Racah type and the \(\mu \)-conjecture. Zbl 1194.15013
Nomura, Kazumasa; Terwilliger, Paul
7
2010
Billiard arrays and finite-dimensional irreducible \(U_q(\mathfrak{sl}_2)\)-modules. Zbl 1352.17021
Terwilliger, Paul
7
2014
The classification of distance-regular graphs of type IIB. Zbl 0727.05050
Terwilliger, P.
7
1988
The \(Q\)-polynomial idempotents of a distance-regular graph. Zbl 1205.05069
Jurišić, Aleksandar; Terwilliger, Paul; Žitnik, Arjana
6
2010
Transition maps between the 24 bases for a Leonard pair. Zbl 1169.05055
Nomura, Kazumasa; Terwilliger, Paul
6
2009
The pseudo-cosine sequences of a distance-regular graph. Zbl 1110.05105
Pascasio, Arlene A.; Terwilliger, Paul
6
2006
The universal DAHA of type \((C_1^\vee, C_1)\) and Leonard pairs of \(q\)-Racah type. Zbl 1371.33031
Nomura, Kazumasa; Terwilliger, Paul
6
2017
The quantum adjacency algebra and subconstituent algebra of a graph. Zbl 1416.05142
Terwilliger, Paul; Žitnik, Arjana
6
2019
The alternating PBW basis for the positive part of \(U_q(\hat{\mathfrak{s} \mathfrak{l}}_2)\). Zbl 1421.82012
Terwilliger, Paul
6
2019
Lowering-raising triples and \(U_q(\mathfrak{sl}_2)\). Zbl 1358.17021
Terwilliger, Paul
5
2015
On the shape of a tridiagonal pair. Zbl 1186.15003
Nomura, Kazumasa; Terwilliger, Paul
5
2010
Quantum matroids. Zbl 0855.06004
Terwilliger, Paul
5
1996
\(P\)- and \(\mathcal Q\)-polynomial association schemes and their antipodal \(P\)- polynomial covers. Zbl 0779.05058
Terwilliger, Paul
5
1993
A class of distance-regular graphs that are \(\phi\)-polynomial. Zbl 0579.05029
Terwilliger, Paul
5
1986
The alternating central extension for the positive part of \(U_q(\hat{\mathfrak{sl}}_2)\). Zbl 1440.81053
Terwilliger, Paul
5
2019
The alternating central extension of the \(q\)-Onsager algebra. Zbl 1487.17047
Terwilliger, Paul
3
2021
Totally bipartite tridiagonal pairs. Zbl 07373356
Nomura, Kazumasa; Terwilliger, Paul
3
2021
A conjecture concerning the \(q\)-Onsager algebra. Zbl 1487.17036
Terwilliger, Paul
2
2021
The Norton algebra of a \(Q\)-polynomial distance-regular graph. Zbl 1479.05372
Terwilliger, Paul
2
2021
Leonard pairs, spin models, and distance-regular graphs. Zbl 1448.05064
Nomura, Kazumasa; Terwilliger, Paul
2
2021
Tridiagonal pairs of \(q\)-Racah-type and the \(q\)-tetrahedron algebra. Zbl 1481.17025
Terwilliger, Paul
1
2021
Idempotent systems. Zbl 07357258
Nomura, Kazumasa; Terwilliger, Paul
1
2021
An infinite-dimensional \(\square_q\)-module obtained from the \(q\)-shuffle algebra for affine \(\mathfrak{sl}_2\). Zbl 1487.17032
Post, Sarah; Terwilliger, Paul
1
2020
The quantum adjacency algebra and subconstituent algebra of a graph. Zbl 1416.05142
Terwilliger, Paul; Žitnik, Arjana
6
2019
The alternating PBW basis for the positive part of \(U_q(\hat{\mathfrak{s} \mathfrak{l}}_2)\). Zbl 1421.82012
Terwilliger, Paul
6
2019
The alternating central extension for the positive part of \(U_q(\hat{\mathfrak{sl}}_2)\). Zbl 1440.81053
Terwilliger, Paul
5
2019
Using Catalan words and a \(q\)-shuffle algebra to describe a PBW basis for the positive part of \(U_q(\widehat{\mathfrak{sl}}_2)\). Zbl 1462.17021
Terwilliger, Paul
5
2019
Self-dual Leonard pairs. Zbl 1454.15010
Nomura, Kazumasa; Terwilliger, Paul
1
2019
The Lusztig automorphism of the \(q\)-Onsager algebra. Zbl 1464.17022
Terwilliger, Paul
13
2018
The \(q\)-Onsager algebra and the universal Askey-Wilson algebra. Zbl 1390.33038
Terwilliger, Paul
13
2018
An action of the free product \(\mathbb{Z}_2 \star \mathbb{Z}_2 \star \mathbb{Z}_2\) on the \(q\)-Onsager algebra and its current algebra. Zbl 1400.81123
Terwilliger, Paul
5
2018
A poset \(\Phi_{n}\) whose maximal chains are in bijection with the \(n\times n\) alternating sign matrices. Zbl 1392.05021
Terwilliger, Paul
2
2018
Tridiagonal pairs of \(q\)-Racah type, the Bockting operator {\(\psi\)}, and \(L\)-operators for \(U_{q}(L(\mathfrak{sl}_{2}))\). Zbl 1426.17011
Terwilliger, Paul
2
2018
The \(q\)-Onsager algebra and the positive part of \(U_q(\hat{\mathfrak{sl}}_2)\). Zbl 1386.17018
Terwilliger, Paul
13
2017
The universal DAHA of type \((C_1^\vee, C_1)\) and Leonard pairs of \(q\)-Racah type. Zbl 1371.33031
Nomura, Kazumasa; Terwilliger, Paul
6
2017
The Lusztig automorphism of \(U_q(\mathfrak{sl}_2)\) from the equitable point of view. Zbl 1386.17019
Terwilliger, Paul
4
2017
Leonard triples of \(q\)-Racah type and their pseudo intertwiners. Zbl 1352.15015
Terwilliger, Paul
2
2017
Lowering-raising triples and \(U_q(\mathfrak{sl}_2)\). Zbl 1358.17021
Terwilliger, Paul
5
2015
Evaluation modules for the \(q\)-tetrahedron algebra. Zbl 1294.17014
Ito, Tatsuro; Rosengren, Hjalmar; Terwilliger, Paul
16
2014
Distance-regular graphs of \(q\)-Racah type and the universal Askey-Wilson algebra. Zbl 1295.05100
Terwilliger, Paul; Žitnik, Arjana
10
2014
The algebra \(U_q(\mathfrak{sl}_2)\) in disguise. Zbl 1348.17011
Bockting-Conrad, Sarah; Terwilliger, Paul
9
2014
Billiard arrays and finite-dimensional irreducible \(U_q(\mathfrak{sl}_2)\)-modules. Zbl 1352.17021
Terwilliger, Paul
7
2014
The universal Askey-Wilson algebra and DAHA of type \((C_{1}^{\vee },C_{1})\). Zbl 1293.33022
Terwilliger, Paul
26
2013
Finite-dimensional irreducible \(U_q(\mathfrak{sl}_2)\)-modules from the equitable point of view. Zbl 1354.17012
Terwilliger, Paul
15
2013
Bipartite \(Q\)-polynomial distance-regular graphs and uniform posets. Zbl 1271.05105
Miklavič, Štefko; Terwilliger, Paul
7
2013
Augmented down-up algebras and uniform posets. Zbl 1310.06003
Terwilliger, Paul; Worawannotai, Chalermpong
4
2013
Krawtchouk polynomials, the Lie algebra \(\mathfrak{sl}_2\), and Leonard pairs. Zbl 1261.33001
Nomura, Kazumasa; Terwilliger, Paul
12
2012
The Rahman polynomials and the Lie algebra \(\mathfrak{sl}_{3}(\mathbb{C})\). Zbl 1353.33007
Iliev, Plamen; Terwilliger, Paul
11
2012
The universal Askey-Wilson algebra. Zbl 1244.33015
Terwilliger, Paul
43
2011
The universal Askey-Wilson algebra and the equitable presentation of \(U_{q}(sl_{2})\). Zbl 1244.33016
Terwilliger, Paul
26
2011
A classification of sharp tridiagonal pairs. Zbl 1225.15015
Ito, Tatsuro; Nomura, Kazumasa; Terwilliger, Paul
20
2011
The equitable basis for \({\mathfrak{sl}_2}\). Zbl 1277.17013
Benkart, Georgia; Terwilliger, Paul
18
2011
Tridiagonal matrices with nonnegative entries. Zbl 1219.15023
Nomura, Kazumasa; Terwilliger, Paul
4
2011
Mock tridiagonal systems. Zbl 1233.15003
Ito, Tatsuro; Terwilliger, Paul
2
2011
The augmented tridiagonal algebra. Zbl 1236.17022
Ito, Tatsuro; Terwilliger, Paul
40
2010
Double affine Hecke algebras of rank 1 and the \(\mathbb Z_3\)-symmetric Askey-Wilson relations. Zbl 1220.33018
Ito, Tatsuro; Terwilliger, Paul
15
2010
Tridiagonal pairs of \(q\)-Racah type and the \(\mu \)-conjecture. Zbl 1194.15013
Nomura, Kazumasa; Terwilliger, Paul
7
2010
The \(Q\)-polynomial idempotents of a distance-regular graph. Zbl 1205.05069
Jurišić, Aleksandar; Terwilliger, Paul; Žitnik, Arjana
6
2010
On the shape of a tridiagonal pair. Zbl 1186.15003
Nomura, Kazumasa; Terwilliger, Paul
5
2010
How to sharpen a tridiagonal pair. Zbl 1237.15012
Ito, Tatsuro; Terwilliger, Paul
4
2010
Distance-regular graphs with light tails. Zbl 1225.05255
Jurišić, Aleksandar; Terwilliger, Paul; Žitnik, Arjana
2
2010
An algebra generated by two sets of mutually orthogonal idempotents. Zbl 1239.16027
Ito, Tatsuro; Terwilliger, Paul
1
2010
Tridiagonal pairs of \(q\)-Racah type. Zbl 1177.33021
Ito, Tatsuro; Terwilliger, Paul
29
2009
Distance-regular graphs and the \(q\)-tetrahedron algebra. Zbl 1193.17008
Ito, Tatsuro; Terwilliger, Paul
24
2009
Distance-regular graphs of \(q\)-Racah type and the \(q\)-tetrahedron algebra. Zbl 1206.05103
Ito, Tatsuro; Terwilliger, Paul
10
2009
The Drinfel’d polynomial of a tridiagonal pair. Zbl 1271.15003
Ito, Tatsuro; Terwilliger, Paul
9
2009
Tridiagonal pairs and the \(\mu \)-conjecture. Zbl 1155.15011
Nomura, Kazumasa; Terwilliger, Paul
8
2009
Transition maps between the 24 bases for a Leonard pair. Zbl 1169.05055
Nomura, Kazumasa; Terwilliger, Paul
6
2009
Finite-dimensional irreducible modules for the three-point \(\mathfrak{sl}_2\) loop algebra. Zbl 1207.17030
Ito, Tatsuro; Terwilliger, Paul
30
2008
Sharp tridiagonal pairs. Zbl 1193.05164
Nomura, Kazumasa; Terwilliger, Paul
20
2008
The structure of a tridiagonal pair. Zbl 1144.05331
Nomura, Kazumasa; Terwilliger, Paul
20
2008
The switching element for a Leonard pair. Zbl 1134.05105
Nomura, Kazumasa; Terwilliger, Paul
16
2008
Towards a classification of the tridiagonal pairs. Zbl 1193.05165
Nomura, Kazumasa; Terwilliger, Paul
15
2008
The subconstituent algebra of a bipartite distance-regular graph; thin modules with endpoint two. Zbl 1136.05076
MacLean, Mark S.; Terwilliger, Paul
8
2008
Pseudo 1-homogeneous distance-regular graphs. Zbl 1160.05060
Jurišić, Aleksandar; Terwilliger, Paul
2
2008
Tridiagonal pairs and the quantum affine algebra \(U_q(\widehat{\text{sl}}_2)\). Zbl 1128.16028
Ito, Tatsuro; Terwilliger, Paul
64
2007
The \(q\)-tetrahedron algebra and its finite dimensional irreducible modules. Zbl 1133.17011
Ito, Tatsuro; Terwilliger, Paul
44
2007
The tetrahedron algebra, the Onsager algebra, and the \(\mathfrak{sl}_2\) loop algebra. Zbl 1163.17026
Hartwig, Brian; Terwilliger, Paul
44
2007
Two non-nilpotent linear transformations that satisfy the cubic \(q\)-Serre relations. Zbl 1179.17017
Ito, Tatsuro; Terwilliger, Paul
44
2007
Linear transformations that are tridiagonal with respect to both eigenbases of a Leonard pair. Zbl 1119.05111
Nomura, Kazumasa; Terwilliger, Paul
38
2007
Affine transformations of a Leonard pair. Zbl 1143.05337
Nomura, Kazumasa; Terwilliger, Paul
23
2007
The universal central extension of the three-point \(\mathfrak{sl}_2\) loop algebra. Zbl 1153.17008
Benkart, Georgia; Terwilliger, Paul
21
2007
\(p\)-inverting pairs of linear transformations and the \(q\)-tetrahedron algebra. Zbl 1146.17009
Ito, Tatsuro; Terwilliger, Paul
20
2007
Tridiagonal pairs of Krawtchouk type. Zbl 1132.15010
Ito, Tatsuro; Terwilliger, Paul
20
2007
Balanced Leonard pairs. Zbl 1119.05110
Nomura, Kazumasa; Terwilliger, Paul
20
2007
The split decomposition of a tridiagonal pair. Zbl 1127.05108
Nomura, Kazumasa; Terwilliger, Paul
17
2007
Almost-bipartite distance-regular graphs with the \(Q\)-polynomial property. Zbl 1124.05095
Lang, Michael S.; Terwilliger, Paul M.
4
2007
An algebraic approach to the Askey scheme of orthogonal polynomials. Zbl 1102.33011
Terwilliger, Paul
69
2006
The quantum algebra \(U_q(\mathfrak{sl}_2)\) and its equitable presentation. Zbl 1090.17004
Ito, Tatsuro; Terwilliger, Paul; Weng, Chih-Wen
51
2006
The equitable presentation for the quantum group associated with a symmetrizable Kac-Moody algebra. Zbl 1106.17021
Terwilliger, Paul
32
2006
Some trace formulae involving the split sequences of a Leonard pair. Zbl 1085.05070
Nomura, Kazumasa; Terwilliger, Paul
20
2006
Matrix units associated with the split basis of a Leonard pair. Zbl 1107.05103
Nomura, Kazumasa; Terwilliger, Paul
19
2006
The determinant of \(AA^{*} - A^{*}A\) for a Leonard pair \(A,A^{*}\). Zbl 1108.15007
Nomura, Kazumasa; Terwilliger, Paul
15
2006
Taut distance-regular graphs and the subconstituent algebra. Zbl 1100.05104
MacLean, Mark S.; Terwilliger, Paul
10
2006
The pseudo-cosine sequences of a distance-regular graph. Zbl 1110.05105
Pascasio, Arlene A.; Terwilliger, Paul
6
2006
Two linear transformations each tridiagonal with respect to an eigenbasis of the other; comments on the parameter array. Zbl 1063.05138
Terwilliger, Paul
77
2005
Two linear transformations each tridiagonal with respect to an eigenbasis of the other; the TD-D canonical form and the LB-UB canonical form. Zbl 1079.15005
Terwilliger, Paul
51
2005
Two linear transformations each tridiagonal with respect to an eigenbasis of the other: comments on the split decomposition. Zbl 1069.15005
Terwilliger, Paul
33
2005
The Terwilliger algebra of an almost-bipartite \(P\)- and \(Q\)-polynomial association scheme. Zbl 1063.05135
Caughman, John S.; Maclean, Mark S.; Terwilliger, Paul M.
17
2005
The displacement and split decompositions for a \(Q\)-polynomial distance-regular graph. Zbl 1065.05097
Terwilliger, Paul
17
2005
An inequality for regular near polygons. Zbl 1061.05105
Terwilliger, Paul; Weng, Chih-wen
1
2005
Leonard pairs and the Askey-Wilson relations. Zbl 1062.33018
Terwilliger, Paul; Vidunas, Raimundas
92
2004
Leonard pairs and the \(q\)-Racah polynomials. Zbl 1075.05090
Terwilliger, Paul
69
2004
The shape of a tridiagonal pair. Zbl 1037.17013
Ito, Tatsuro; Terwilliger, Paul
46
2004
Irreducible modules for the quantum affine algebra \(U_{q}(\mathfrak {\widehat{sl}_2})\) and its Borel subalgebra. Zbl 1106.17014
Benkart, Georgia; Terwilliger, Paul
20
2004
An inequality involving the local eigenvalues of a distance-regular graph. Zbl 1047.05045
Terwilliger, Paul
8
2004
Distance-regular graphs, pseudo primitive idempotents, and the Terwilliger algebra. Zbl 1035.05104
Terwilliger, Paul; Weng, Chih-wen
8
2004
Introduction to Leonard pairs. Zbl 1035.05103
Terwilliger, Paul
59
2003
Leonard pairs from 24 points of view. Zbl 1040.05030
Terwilliger, Paul
61
2002
Tight distance-regular graphs and the subconstituent algebra. Zbl 1014.05070
Go, Junie T.; Terwilliger, Paul
29
2002
The subconstituent algebra of a distance-regular graph; thin modules with endpoint one. Zbl 1011.05066
Terwilliger, Paul
11
2002
Two linear transformations each tridiagonal with respect to an eigenbasis of the other. Zbl 0980.05054
Terwilliger, Paul
159
2001
Some algebra related to \(P\)- and \(Q\)-polynomial association schemes. Zbl 0995.05148
Ito, Tatsuro; Tanabe, Kenichiro; Terwilliger, Paul
109
2001
Two relations that generalize the \(q\)-Serre relations and the Dolan-Grady relations. Zbl 1061.16033
Terwilliger, Paul
91
2001
Tight distance-regular graphs. Zbl 0959.05121
Jurišić, Aleksandar; Koolen, Jack; Terwilliger, Paul
43
2000
...and 28 more Documents
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Cited by 357 Authors

106 Terwilliger, Paul M.
42 Vinet, Luc
37 Nomura, Kazumasa
36 Koolen, Jack H.
30 Hou, Bo
30 Zhedanov, Alexei S.
28 Gao, Suogang
27 Baseilhac, Pascal
24 Ito, Tatsuro
21 Miklavič, Štefko
20 Curtin, Brian
16 Tanaka, Hajime
15 Huang, Hau-wen
15 Jurišić, Aleksandar
15 MacLean, Mark S.
13 Crampé, Nicolas
13 Weng, Chih-Wen
12 Suzuki, Hiroshi
10 Xu, Bangteng
9 Genest, Vincent X.
9 Tsujimoto, Satoshi
8 Alnajjar, Hasan
8 Bannai, Eiichi
8 Hiraki, Akira
7 Bockting-Conrad, Sarah
7 Caughman, John S. IV
7 Deza, Michel Marie
7 Gavrilyuk, Alexander L.
6 Bang, Sejeong
6 Hou, Lihang
6 Jordan, David Alan
6 Kang, Na
6 Lang, Michael S.
6 Lee, Jaeho
6 Morales, John Vincent S.
6 Pascasio, Arlene A.
6 Penjic, Safet
6 Suda, Sho
5 Bannai, Etsuko
5 Belliard, Samuel
5 Gaboriaud, Julien
5 Laurent, Monique
5 Liang, Xiaoye
5 Makhnëv, Aleksandr Alekseevich
5 Park, Jongyook
5 Tan, Yingying
5 Žitnik, Arjana
4 Benkart, Georgia M.
4 Bergeron, Geoffroy
4 Funk-Neubauer, Darren
4 Hanson, Edward
4 Iliev, Plamen
4 Kim, Kijung
4 Lu, Ming
4 Martin, William J.
4 Moulton, Vincent L.
4 Neumaier, Arnold
4 Pan, Yeh-jong
4 van de Vijver, Wouter
4 Wang, Kaishun
4 Watanabe, Yuta
3 Brouwer, Andries Evert
3 Cantuba, Rafael Reno S.
3 Chen, Xinhong
3 De Bie, Hendrik
3 De Clercq, Hadewijch
3 Fernández, Blas
3 Godjali, Ali
3 Hartwig, Brian
3 Ivanov, Alexander A.
3 Koizumi, Kozo
3 Leanos, Jesus
3 Lv, Benjian
3 Ma, Jianmin
3 Maldonado, Carolina
3 Post, Sarah
3 Samuelson, Peter
3 Sasaki, Ryu
3 Tanaka, Rie
3 Tomiyama, Masato
3 Tsuboi, Zengo
3 Van Dam, Edwin Robert
3 Vanhove, Frédéric
3 Vidali, Janoš
3 Vidunas, Raimundas
3 Vu, Thi Thao
3 Wang, Yan
3 Williford, Jason S.
3 Yang, Yang
3 Yu, Hyonju
2 Avis, David M.
2 Balaji, Srinivasan
2 Berest, Yuri Yu.
2 Blau, Harvey I.
2 Cámara, Marc
2 Coolsaet, Kris
2 Cox, Ben Lewis
2 Daqqa, Ibtisam
2 Dickie, Garth A.
2 Ding, Kequan
...and 257 more Authors
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Cited in 102 Serials

110 Linear Algebra and its Applications
61 European Journal of Combinatorics
41 Journal of Algebraic Combinatorics
33 Discrete Mathematics
32 Journal of Algebra
26 Graphs and Combinatorics
22 Nuclear Physics. B
22 Journal of Combinatorial Theory. Series B
18 Journal of Mathematical Physics
18 Journal of Combinatorial Theory. Series A
17 Communications in Algebra
15 The Electronic Journal of Combinatorics
13 Letters in Mathematical Physics
13 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications
12 Linear and Multilinear Algebra
9 Communications in Mathematical Physics
9 Journal of Algebra and its Applications
8 Designs, Codes and Cryptography
7 Proceedings of the American Mathematical Society
7 Combinatorica
7 The Ramanujan Journal
6 Transactions of the American Mathematical Society
6 Ars Mathematica Contemporanea
5 Advances in Mathematics
5 Journal of Computational and Applied Mathematics
4 Journal of Pure and Applied Algebra
4 Annales Henri Poincaré
3 Compositio Mathematica
3 Advances in Applied Mathematics
3 ELA. The Electronic Journal of Linear Algebra
3 Algebras and Representation Theory
3 Journal of Statistical Mechanics: Theory and Experiment
2 Discrete Applied Mathematics
2 Journal of Mathematical Analysis and Applications
2 Reviews in Mathematical Physics
2 Acta Applicandae Mathematicae
2 Constructive Approximation
2 Mathematical Programming. Series A. Series B
2 Transformation Groups
2 Doklady Mathematics
2 Journal of Nonlinear Mathematical Physics
2 Proceedings of the Steklov Institute of Mathematics
2 Journal of Physics A: Mathematical and Theoretical
2 Science China. Mathematics
2 Algebraic Combinatorics
1 Indian Journal of Pure & Applied Mathematics
1 Israel Journal of Mathematics
1 Journal of Statistical Physics
1 Mathematical Notes
1 Physics Letters. A
1 Physics Letters. B
1 Reports on Mathematical Physics
1 Rocky Mountain Journal of Mathematics
1 Mathematics of Computation
1 Journal of Geometry and Physics
1 Annals of the Institute of Statistical Mathematics
1 Bulletin of the London Mathematical Society
1 Canadian Mathematical Bulletin
1 Colloquium Mathematicum
1 Duke Mathematical Journal
1 Geometriae Dedicata
1 Glasgow Mathematical Journal
1 International Journal of Mathematics and Mathematical Sciences
1 Inventiones Mathematicae
1 Journal of Soviet Mathematics
1 Mathematische Zeitschrift
1 Michigan Mathematical Journal
1 Networks
1 Osaka Journal of Mathematics
1 Siberian Mathematical Journal
1 Studies in Applied Mathematics
1 Bulletin of the Korean Mathematical Society
1 Statistics & Probability Letters
1 Chinese Annals of Mathematics. Series B
1 Acta Mathematicae Applicatae Sinica. English Series
1 Discrete & Computational Geometry
1 Sugaku Expositions
1 International Journal of Mathematics
1 Computational Geometry
1 Expositiones Mathematicae
1 Journal of Knot Theory and its Ramifications
1 The Australasian Journal of Combinatorics
1 Test
1 Applied Categorical Structures
1 Algebra Colloquium
1 St. Petersburg Mathematical Journal
1 Séminaire Lotharingien de Combinatoire
1 Annals of Combinatorics
1 Communications of the Korean Mathematical Society
1 Acta Mathematica Sinica. English Series
1 Communications in Contemporary Mathematics
1 Journal of Applied Mathematics and Computing
1 Algebra and Discrete Mathematics
1 Statistical Methods and Applications
1 The European Physical Journal B. Condensed Matter and Complex Systems
1 International Electronic Journal of Algebra (IEJA)
1 Analysis and Mathematical Physics
1 Arabian Journal of Mathematics
1 Forum of Mathematics, Sigma
1 JSIAM Letters
...and 2 more Serials
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Cited in 38 Fields

384 Combinatorics (05-XX)
150 Nonassociative rings and algebras (17-XX)
143 Special functions (33-XX)
99 Linear and multilinear algebra; matrix theory (15-XX)
91 Quantum theory (81-XX)
60 Associative rings and algebras (16-XX)
46 Group theory and generalizations (20-XX)
24 Statistical mechanics, structure of matter (82-XX)
13 Harmonic analysis on Euclidean spaces (42-XX)
12 Geometry (51-XX)
10 Order, lattices, ordered algebraic structures (06-XX)
10 Difference and functional equations (39-XX)
10 Operator theory (47-XX)
10 Information and communication theory, circuits (94-XX)
8 Topological groups, Lie groups (22-XX)
8 Convex and discrete geometry (52-XX)
7 Manifolds and cell complexes (57-XX)
7 Operations research, mathematical programming (90-XX)
6 Algebraic geometry (14-XX)
6 Probability theory and stochastic processes (60-XX)
5 Number theory (11-XX)
5 Commutative algebra (13-XX)
5 Dynamical systems and ergodic theory (37-XX)
3 Functional analysis (46-XX)
3 Numerical analysis (65-XX)
3 Relativity and gravitational theory (83-XX)
2 \(K\)-theory (19-XX)
2 Functions of a complex variable (30-XX)
2 Ordinary differential equations (34-XX)
2 Partial differential equations (35-XX)
2 Differential geometry (53-XX)
2 Algebraic topology (55-XX)
2 Statistics (62-XX)
1 General algebraic systems (08-XX)
1 Category theory; homological algebra (18-XX)
1 Several complex variables and analytic spaces (32-XX)
1 Computer science (68-XX)
1 Mechanics of particles and systems (70-XX)

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