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## Humphreys, James E.

Compute Distance To:
 Author ID: humphreys.james-e Published as: Humphreys, J. E.; Humphreys, James E. Homepage: http://people.math.umass.edu/~jeh/ External Links: MGP · Wikidata · MathOverflow · dblp · GND
 Documents Indexed: 59 Publications since 1967, including 16 Books

#### Co-Authors

 57 single-authored 1 Jantzen, Jens Carsten 1 Verma, Daya-Nand
all top 5

#### Serials

 9 Journal of Algebra 5 Graduate Texts in Mathematics 3 Communications in Algebra 2 American Mathematical Monthly 2 Bulletin of the American Mathematical Society. New Series 2 Bulletin of the American Mathematical Society 2 Cambridge Studies in Advanced Mathematics 2 Lecture Notes in Mathematics 1 Communications on Pure and Applied Mathematics 1 Advances in Mathematics 1 Bulletin of the London Mathematical Society 1 Canadian Journal of Mathematics 1 Journal of the London Mathematical Society. Second Series 1 Journal of Pure and Applied Algebra 1 Mathematische Zeitschrift 1 Memoirs of the American Mathematical Society 1 Pacific Journal of Mathematics 1 Proceedings of the American Mathematical Society 1 Experimental Mathematics 1 Graduate Studies in Mathematics 1 London Mathematical Society Lecture Note Series 1 Mathematical Surveys and Monographs 1 Nederlandse Akademie van Wetenschappen. Proceedings. Series A. Indagationes Mathematicae
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#### Fields

 48 Group theory and generalizations (20-XX) 22 Nonassociative rings and algebras (17-XX) 10 Algebraic geometry (14-XX) 9 Topological groups, Lie groups (22-XX) 2 Number theory (11-XX) 2 Associative rings and algebras (16-XX) 2 Category theory; homological algebra (18-XX) 2 Geometry (51-XX)

#### Citations contained in zbMATH Open

54 Publications have been cited 4,113 times in 3,708 Documents Cited by Year
Introduction to Lie algebras and representation theory. Zbl 0254.17004
Humphreys, J. E.
1972
Reflection groups and Coxeter groups. Zbl 0725.20028
Humphreys, James E.
1990
Linear algebraic groups. Zbl 0325.20039
Humphreys, James E.
1975
Introduction to Lie algebras and representation theory. 2nd printing, rev. Zbl 0447.17001
Humphreys, James E.
1978
Linear algebraic groups. (Linejnye algebraicheskie gruppy). Transl. from the English by A. E. Zalesskij. Zbl 0507.20017
Humphreys, J. E.
1980
Representations of semisimple Lie algebras in the BGG category $$\mathcal O$$. Zbl 1177.17001
Humphreys, James E.
2008
Conjugacy classes in semisimple algebraic groups. Zbl 0834.20048
Humphreys, James E.
1995
Reflection groups and Coxeter groups. Zbl 0768.20016
Humphreys, James E.
1992
Linear algebraic groups. Corr. 2nd printing. Zbl 0471.20029
Humphreys, James E.
1981
Introduction to Lie algebras and representation theory. 3rd printing, rev. Zbl 0447.17002
Humphreys, James E.
1980
Modular representations of finite groups of Lie type. Zbl 1113.20016
Humphreys, James E.
2006
Modular representations of classical Lie algebras and semi-simple groups. Zbl 0219.17003
Humphreys, J. E.
1971
Ordinary and modular representations of Chevalley groups. Zbl 0341.20037
Humphreys, James E.
1976
Comparing modular representations of semisimple groups and their Lie algebras. Zbl 0919.17013
Humphreys, J. E.
1997
Algebraic groups and modular Lie algebras. Zbl 0173.03001
Humphreys, J. E.
1967
Finite and infinite dimensional modules for semisimple Lie algebras. Zbl 0392.17006
Humphreys, J. E.
1978
Defect groups for finite groups of Lie type. Zbl 0198.04502
Humphreys, J. E.
1971
On the authomorphisms of infinite Chevalley groups. Zbl 0181.03803
Humphreys, J. E.
1969
Projective modules for SL(2,q). Zbl 0258.20010
Humphreys, J. E.
1973
Symmetry for finite dimensional Hopf algebras. Zbl 0349.16001
Humphreys, J. E.
1978
The Steinberg representation. Zbl 0627.20024
Humphreys, J. E.
1987
Modular representations of simple Lie algebras. Zbl 0962.17013
Humphreys, J. E.
1998
Modular representations of finite groups of Lie type. Zbl 0472.20015
Humphreys, J. E.
1980
Arithmetic groups. Zbl 0426.20029
Humphreys, James E.
1980
Blocks and indecomposable modules for semisimple algebraic groups. Zbl 0398.20047
Humphreys, J. E.; Jantzen, J. C.
1978
Remarks on ”A theorem on special linear groups”. Zbl 0237.20045
Humphreys, J. E.
1972
Ordinary and modular characters of $$\mathrm{SL}(3,p)$$. Zbl 0474.20021
Humphreys, J. E.
1981
Projective modules for finite Chevalley groups. Zbl 0258.20007
Humphreys, J. E.; Verma, D. N.
1973
On the hyperalgebra of a semi-simple algebraic group. Zbl 0367.20043
Humphreys, J. E.
1977
Existence of Levi factors in certain algebraic groups. Zbl 0157.36701
Humphreys, J. E.
1967
Deligne-Lusztig characters and principal indecomposable modules. Zbl 0427.20033
Humphreys, J. E.
1980
Cohomology of G/B in characteristic p. Zbl 0612.20023
Humphreys, J. E.
1986
Modular representations of classical Lie algebras. Zbl 0199.35103
Humphreys, J. E.
1970
On the structure of Weyl modules. Zbl 0546.20036
Humphreys, J. E.
1984
Hilbert’s fourteenth problem. Zbl 0391.14002
Humphreys, J. E.
1978
Representations of SL(2,p). Zbl 0296.20020
Humphreys, J. E.
1975
Cartan invariants. Zbl 0555.20009
Humphreys, J. E.
1985
Some computations of Cartan invariants for finite groups of Lie type. Zbl 0358.20013
Humphreys, J. E.
1973
Restricted Lie algebras (and beyond). Zbl 0501.17007
Humphreys, J. E.
1982
Non-zero $$Ext^ 1$$ for Chevalley groups (via algebraic groups). Zbl 0567.20029
Humphreys, J. E.
1985
Generic Cartan invariants for Frobenius kernels and Chevalley groups. Zbl 0674.20023
Humphreys, J. E.
1989
Cohomology of line bundles on G/B for the exceptional group $$G_ 2$$. Zbl 0615.20023
Humphreys, J. E.
1987
Projective modules for Sp(4,p) in characteristic p. Zbl 0618.20027
Humphreys, J. E.
1986
A construction of projective modules in the category O of Bernstein- Gel’fand-Gel’fand. Zbl 0367.17005
Humphreys, J. E.
1977
Extremal composition factors for groups of Lie type. Zbl 0840.20035
Humphreys, J. E.
1994
Weyl modules and Bott’s theorem in characteristic p. Zbl 0395.20023
Humphreys, J. E.
1978
Arithmetic groups. Zbl 0248.20060
Humphreys, J. E.
1971
Induced modules for semisimple groups and Lie algebras. Zbl 0582.17004
Humphreys, J. E.
1986
Weyl groups, deformations of linkage classes, and character degrees for Chevalley groups. Zbl 0286.20055
Humphreys, J. E.
1974
Cartan invariants and decomposition numbers of Chevalley groups. Zbl 0451.20038
Humphreys, J. E.
1980
Ordinary and modular characters of $$\mathrm{SU}(3,p)$$. Zbl 0699.20032
Humphreys, J. E.
1990
Representations of reduced enveloping algebras and cells in the affine Weyl group. Zbl 1155.17301
Humphreys, J. E.
2006
Another look at Dickson’s invariants for finite linear groups. Zbl 0835.20055
Humphreys, J. E.
1994
Analogues of Weyl’s formula for reduced enveloping algebras. Zbl 1162.17302
Humphreys, J. E.
2002
Representations of semisimple Lie algebras in the BGG category $$\mathcal O$$. Zbl 1177.17001
Humphreys, James E.
2008
Modular representations of finite groups of Lie type. Zbl 1113.20016
Humphreys, James E.
2006
Representations of reduced enveloping algebras and cells in the affine Weyl group. Zbl 1155.17301
Humphreys, J. E.
2006
Analogues of Weyl’s formula for reduced enveloping algebras. Zbl 1162.17302
Humphreys, J. E.
2002
Modular representations of simple Lie algebras. Zbl 0962.17013
Humphreys, J. E.
1998
Comparing modular representations of semisimple groups and their Lie algebras. Zbl 0919.17013
Humphreys, J. E.
1997
Conjugacy classes in semisimple algebraic groups. Zbl 0834.20048
Humphreys, James E.
1995
Extremal composition factors for groups of Lie type. Zbl 0840.20035
Humphreys, J. E.
1994
Another look at Dickson’s invariants for finite linear groups. Zbl 0835.20055
Humphreys, J. E.
1994
Reflection groups and Coxeter groups. Zbl 0768.20016
Humphreys, James E.
1992
Reflection groups and Coxeter groups. Zbl 0725.20028
Humphreys, James E.
1990
Ordinary and modular characters of $$\mathrm{SU}(3,p)$$. Zbl 0699.20032
Humphreys, J. E.
1990
Generic Cartan invariants for Frobenius kernels and Chevalley groups. Zbl 0674.20023
Humphreys, J. E.
1989
The Steinberg representation. Zbl 0627.20024
Humphreys, J. E.
1987
Cohomology of line bundles on G/B for the exceptional group $$G_ 2$$. Zbl 0615.20023
Humphreys, J. E.
1987
Cohomology of G/B in characteristic p. Zbl 0612.20023
Humphreys, J. E.
1986
Projective modules for Sp(4,p) in characteristic p. Zbl 0618.20027
Humphreys, J. E.
1986
Induced modules for semisimple groups and Lie algebras. Zbl 0582.17004
Humphreys, J. E.
1986
Cartan invariants. Zbl 0555.20009
Humphreys, J. E.
1985
Non-zero $$Ext^ 1$$ for Chevalley groups (via algebraic groups). Zbl 0567.20029
Humphreys, J. E.
1985
On the structure of Weyl modules. Zbl 0546.20036
Humphreys, J. E.
1984
Restricted Lie algebras (and beyond). Zbl 0501.17007
Humphreys, J. E.
1982
Linear algebraic groups. Corr. 2nd printing. Zbl 0471.20029
Humphreys, James E.
1981
Ordinary and modular characters of $$\mathrm{SL}(3,p)$$. Zbl 0474.20021
Humphreys, J. E.
1981
Linear algebraic groups. (Linejnye algebraicheskie gruppy). Transl. from the English by A. E. Zalesskij. Zbl 0507.20017
Humphreys, J. E.
1980
Introduction to Lie algebras and representation theory. 3rd printing, rev. Zbl 0447.17002
Humphreys, James E.
1980
Modular representations of finite groups of Lie type. Zbl 0472.20015
Humphreys, J. E.
1980
Arithmetic groups. Zbl 0426.20029
Humphreys, James E.
1980
Deligne-Lusztig characters and principal indecomposable modules. Zbl 0427.20033
Humphreys, J. E.
1980
Cartan invariants and decomposition numbers of Chevalley groups. Zbl 0451.20038
Humphreys, J. E.
1980
Introduction to Lie algebras and representation theory. 2nd printing, rev. Zbl 0447.17001
Humphreys, James E.
1978
Finite and infinite dimensional modules for semisimple Lie algebras. Zbl 0392.17006
Humphreys, J. E.
1978
Symmetry for finite dimensional Hopf algebras. Zbl 0349.16001
Humphreys, J. E.
1978
Blocks and indecomposable modules for semisimple algebraic groups. Zbl 0398.20047
Humphreys, J. E.; Jantzen, J. C.
1978
Hilbert’s fourteenth problem. Zbl 0391.14002
Humphreys, J. E.
1978
Weyl modules and Bott’s theorem in characteristic p. Zbl 0395.20023
Humphreys, J. E.
1978
On the hyperalgebra of a semi-simple algebraic group. Zbl 0367.20043
Humphreys, J. E.
1977
A construction of projective modules in the category O of Bernstein- Gel’fand-Gel’fand. Zbl 0367.17005
Humphreys, J. E.
1977
Ordinary and modular representations of Chevalley groups. Zbl 0341.20037
Humphreys, James E.
1976
Linear algebraic groups. Zbl 0325.20039
Humphreys, James E.
1975
Representations of SL(2,p). Zbl 0296.20020
Humphreys, J. E.
1975
Weyl groups, deformations of linkage classes, and character degrees for Chevalley groups. Zbl 0286.20055
Humphreys, J. E.
1974
Projective modules for SL(2,q). Zbl 0258.20010
Humphreys, J. E.
1973
Projective modules for finite Chevalley groups. Zbl 0258.20007
Humphreys, J. E.; Verma, D. N.
1973
Some computations of Cartan invariants for finite groups of Lie type. Zbl 0358.20013
Humphreys, J. E.
1973
Introduction to Lie algebras and representation theory. Zbl 0254.17004
Humphreys, J. E.
1972
Remarks on ”A theorem on special linear groups”. Zbl 0237.20045
Humphreys, J. E.
1972
Modular representations of classical Lie algebras and semi-simple groups. Zbl 0219.17003
Humphreys, J. E.
1971
Defect groups for finite groups of Lie type. Zbl 0198.04502
Humphreys, J. E.
1971
Arithmetic groups. Zbl 0248.20060
Humphreys, J. E.
1971
Modular representations of classical Lie algebras. Zbl 0199.35103
Humphreys, J. E.
1970
On the authomorphisms of infinite Chevalley groups. Zbl 0181.03803
Humphreys, J. E.
1969
Algebraic groups and modular Lie algebras. Zbl 0173.03001
Humphreys, J. E.
1967
Existence of Levi factors in certain algebraic groups. Zbl 0157.36701
Humphreys, J. E.
1967
all top 5

#### Cited by 3,500 Authors

 30 Brenti, Francesco 24 Nakano, Daniel K. 24 Putcha, Mohan S. 19 Biswas, Indranil 18 Donkin, Stephen 16 Green, Richard M. 16 Humphreys, James E. 16 Kannan, Subramaniam Senthamarai 16 Mazorchuk, Volodymyr 15 Farnsteiner, Rolf 14 Andersen, Henning Haahr 14 Borovik, Alexandre V. 14 de Graaf, Willem Adriaan 13 Bunina, E. I. 13 Coulembier, Kevin 13 Marberg, Eric 13 Reiner, Victor 13 Roichman, Yuval 13 Stroppel, Catharina H. 12 Billey, Sara C. 12 Guralnick, Robert Michael 12 Hohlweg, Christophe 12 Marietti, Mario 12 Renner, Lex E. 11 Chari, Vyjayanthi 11 Hultman, Axel 11 Malle, Gunter 11 Papi, Paolo 11 Pillen, Cornelius 11 Premet, Alexander A. 11 Shi, Jianyi 11 Singer, Michael F. 11 Testerman, Donna M. 11 Zhao, Kaiming 10 Azam, Saeid 10 Bendel, Christopher P. 10 Dyer, Matthew J. 10 Shu, Bin 10 Stembridge, John R. 10 Tiep Pham Huu 10 Vavilov, Nikolaĭ Aleksandrovich 10 Wang, Dengyin 10 Zalesski, Alexandre Efimovich 9 Adin, Ron M. 9 Benkart, Georgia M. 9 Caselli, Fabrizio 9 Chen, Zhengxin 9 Hare, Kathryn E. 9 Helminck, Aloysius G. 9 Hosaka, Tetsuya 9 Huang, Wenxue 9 Khare, Apoorva 9 Lin, Zongzhu 9 McNinch, George J. 9 Parshall, Brian J. 9 Proctor, Robert A. 9 Reading, Nathan 9 Sentinelli, Paolo 9 Snow, Dennis M. 9 Terwilliger, Paul M. 9 Williamson, Geordie 8 Carnovale, Giovanna 8 Chastkofsky, Leonard 8 Douglas, Andrew S. 8 Draper, Cristina 8 Elduque, Alberto 8 Jantzen, Jens Carsten 8 Larsen, Michael Jeffrey 8 Musson, Ian M. 8 Navarro, Gabriel 8 Navarro, Rosa María 8 Panyushev, Dmitri Ivanovich 8 Repka, Joe 8 Sobaje, Paul 7 Altınel, Tuna 7 Athanasiadis, Christos A. 7 Biagioli, Riccardo 7 Burness, Timothy C. 7 Cellini, Paola 7 Dechant, Pierre-Philippe 7 Deckhart, Robert W. 7 Donnelly, Robert G. 7 Doty, Stephen R. 7 Eswara Rao, Senapathi 7 Guillemin, Victor W. 7 Kaneda, Masaharu 7 Komori, Yasushi 7 Lam, Thomas F. 7 Li, Haisheng 7 Postnikov, Alexander 7 Simson, Daniel 7 Stump, Christian 7 Xu, Xiaoping 6 Andruskiewitsch, Nicolás 6 Benito, Pilar 6 Bergeron, Nantel 6 Boe, Brian Douglas 6 Bremner, Murray R. 6 Breuil, Christophe 6 Brown, Kenneth Alexander ...and 3,400 more Authors
all top 5

#### Cited in 344 Serials

 570 Journal of Algebra 193 Communications in Algebra 171 Transactions of the American Mathematical Society 157 Advances in Mathematics 133 Journal of Pure and Applied Algebra 94 Linear Algebra and its Applications 87 Proceedings of the American Mathematical Society 83 Mathematische Zeitschrift 65 Journal of Algebraic Combinatorics 63 Journal of Combinatorial Theory. Series A 56 Communications in Mathematical Physics 53 Inventiones Mathematicae 52 Annales de l’Institut Fourier 51 Mathematische Annalen 50 Duke Mathematical Journal 48 Transformation Groups 45 Representation Theory 44 Israel Journal of Mathematics 43 Journal of Mathematical Physics 41 Advances in Applied Mathematics 40 European Journal of Combinatorics 39 Algebras and Representation Theory 36 Discrete Mathematics 31 Nuclear Physics. B 29 Compositio Mathematica 29 Journal of Mathematical Sciences (New York) 28 Journal of Geometry and Physics 26 Selecta Mathematica. New Series 25 Linear and Multilinear Algebra 22 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 22 Geometriae Dedicata 22 Journal of Functional Analysis 22 Manuscripta Mathematica 20 Journal of Number Theory 19 Archiv der Mathematik 19 Journal of the American Mathematical Society 18 Mathematical Proceedings of the Cambridge Philosophical Society 18 Journal of Algebra and its Applications 17 Memoirs of the American Mathematical Society 17 Journal of High Energy Physics 16 Letters in Mathematical Physics 16 Siberian Mathematical Journal 16 Tohoku Mathematical Journal. Second Series 16 Indagationes Mathematicae. New Series 16 Journal of Lie Theory 16 Journal of the European Mathematical Society (JEMS) 15 Journal of Symbolic Computation 15 Annals of Combinatorics 13 Differential Geometry and its Applications 13 Annals of Mathematics. Second Series 12 Acta Applicandae Mathematicae 12 Bulletin of the American Mathematical Society. New Series 11 Journal of Differential Equations 11 Proceedings of the Japan Academy. Series A 11 Topology and its Applications 11 International Journal of Algebra and Computation 11 St. Petersburg Mathematical Journal 11 Journal of Group Theory 11 Comptes Rendus. Mathématique. Académie des Sciences, Paris 10 Bulletin of the Australian Mathematical Society 10 Mathematical Notes 10 Algebra and Logic 10 Journal of Soviet Mathematics 10 Publications of the Research Institute for Mathematical Sciences, Kyoto University 10 Proceedings of the Indian Academy of Sciences. Mathematical Sciences 10 Acta Mathematica Sinica. English Series 10 Journal of Nonlinear Mathematical Physics 10 Journal of the Australian Mathematical Society 10 Algebraic Combinatorics 9 Semigroup Forum 9 Discrete & Computational Geometry 9 Science China. Mathematics 8 Reports on Mathematical Physics 8 Mathematics of Computation 8 Journal für die Reine und Angewandte Mathematik 8 International Journal of Mathematics 8 Annals of Physics 8 Expositiones Mathematicae 8 The Electronic Journal of Combinatorics 8 Séminaire Lotharingien de Combinatoire 8 Central European Journal of Mathematics 7 Glasgow Mathematical Journal 7 Results in Mathematics 7 Forum Mathematicum 7 Experimental Mathematics 7 Advances in Applied Clifford Algebras 7 The Ramanujan Journal 7 Communications in Contemporary Mathematics 7 Algebraic & Geometric Topology 7 Journal of the Institute of Mathematics of Jussieu 6 Journal of Mathematical Analysis and Applications 6 Physics Letters. A 6 Rocky Mountain Journal of Mathematics 6 Canadian Journal of Mathematics 6 Publications Mathématiques 6 Monatshefte für Mathematik 6 Nagoya Mathematical Journal 6 Rendiconti del Seminario Matematico della Università di Padova 6 Annals of Global Analysis and Geometry 6 Order ...and 244 more Serials
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#### Cited in 60 Fields

 1,555 Group theory and generalizations (20-XX) 1,193 Nonassociative rings and algebras (17-XX) 615 Algebraic geometry (14-XX) 517 Combinatorics (05-XX) 416 Topological groups, Lie groups (22-XX) 340 Associative rings and algebras (16-XX) 208 Number theory (11-XX) 195 Quantum theory (81-XX) 187 Differential geometry (53-XX) 157 Linear and multilinear algebra; matrix theory (15-XX) 130 Manifolds and cell complexes (57-XX) 123 Convex and discrete geometry (52-XX) 121 Dynamical systems and ergodic theory (37-XX) 114 Commutative algebra (13-XX) 107 Order, lattices, ordered algebraic structures (06-XX) 96 Several complex variables and analytic spaces (32-XX) 85 Special functions (33-XX) 84 Geometry (51-XX) 83 Category theory; homological algebra (18-XX) 71 Global analysis, analysis on manifolds (58-XX) 68 Algebraic topology (55-XX) 58 Abstract harmonic analysis (43-XX) 52 Computer science (68-XX) 51 Field theory and polynomials (12-XX) 48 Ordinary differential equations (34-XX) 38 Probability theory and stochastic processes (60-XX) 37 Functional analysis (46-XX) 35 Partial differential equations (35-XX) 33 Mathematical logic and foundations (03-XX) 32 Statistical mechanics, structure of matter (82-XX) 25 Mechanics of particles and systems (70-XX) 24 $$K$$-theory (19-XX) 22 Relativity and gravitational theory (83-XX) 21 Functions of a complex variable (30-XX) 19 Harmonic analysis on Euclidean spaces (42-XX) 17 Operator theory (47-XX) 17 Information and communication theory, circuits (94-XX) 16 Systems theory; control (93-XX) 15 Numerical analysis (65-XX) 15 Biology and other natural sciences (92-XX) 11 Measure and integration (28-XX) 10 Potential theory (31-XX) 9 General algebraic systems (08-XX) 9 Difference and functional equations (39-XX) 7 Integral transforms, operational calculus (44-XX) 6 Approximations and expansions (41-XX) 5 Operations research, mathematical programming (90-XX) 4 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 3 Real functions (26-XX) 3 Calculus of variations and optimal control; optimization (49-XX) 3 General topology (54-XX) 3 Mechanics of deformable solids (74-XX) 2 Statistics (62-XX) 1 General and overarching topics; collections (00-XX) 1 History and biography (01-XX) 1 Sequences, series, summability (40-XX) 1 Integral equations (45-XX) 1 Fluid mechanics (76-XX) 1 Optics, electromagnetic theory (78-XX) 1 Classical thermodynamics, heat transfer (80-XX)

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