## 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 · IdRef
 Documents Indexed: 59 Publications since 1967, including 16 Books Co-Authors: 2 Co-Authors with 2 Joint Publications 24 Co-Co-Authors

### Co-Authors

 57 single-authored 1 Jantzen, Jens Carsten 1 Verma, Daya-Nand
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### 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 4,457 times in 4,029 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
Representations of semisimple Lie algebras in the BGG category $$\mathcal O$$. Zbl 1177.17001
Humphreys, James E.
2008
Linear algebraic groups. (Linejnye algebraicheskie gruppy). Transl. from the English by A. E. Zalesskij. Zbl 0507.20017
Humphreys, J. E.
1980
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
The Steinberg representation. Zbl 0627.20024
Humphreys, J. E.
1987
Symmetry for finite dimensional Hopf algebras. Zbl 0349.16001
Humphreys, J. E.
1978
Modular representations of simple Lie algebras. Zbl 0962.17013
Humphreys, J. E.
1998
Arithmetic groups. Zbl 0426.20029
Humphreys, James E.
1980
Modular representations of finite groups of Lie type. Zbl 0472.20015
Humphreys, J. 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
Modular representations of classical Lie algebras. Zbl 0199.35103
Humphreys, J. E.
1970
Cohomology of G/B in characteristic p. Zbl 0612.20023
Humphreys, J. E.
1986
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
Non-zero $$Ext^ 1$$ for Chevalley groups (via algebraic groups). Zbl 0567.20029
Humphreys, J. E.
1985
Restricted Lie algebras (and beyond). Zbl 0501.17007
Humphreys, J. E.
1982
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
Generic Cartan invariants for Frobenius kernels and Chevalley groups. Zbl 0674.20023
Humphreys, J. E.
1989
Extremal composition factors for groups of Lie type. Zbl 0840.20035
Humphreys, J. E.
1994
A construction of projective modules in the category O of Bernstein- Gel’fand-Gel’fand. Zbl 0367.17005
Humphreys, J. E.
1977
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
Cartan invariants and decomposition numbers of Chevalley groups. Zbl 0451.20038
Humphreys, J. E.
1980
Weyl groups, deformations of linkage classes, and character degrees for Chevalley groups. Zbl 0286.20055
Humphreys, J. E.
1974
Ordinary and modular characters of $$\mathrm{SU}(3,p)$$. Zbl 0699.20032
Humphreys, J. E.
1990
Another look at Dickson’s invariants for finite linear groups. Zbl 0835.20055
Humphreys, J. E.
1994
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
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
Arithmetic groups. Zbl 0426.20029
Humphreys, James E.
1980
Modular representations of finite groups of Lie type. Zbl 0472.20015
Humphreys, J. 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 3,824 Authors

 32 Nakano, Daniel K. 30 Brenti, Francesco 24 Putcha, Mohan S. 20 Biswas, Indranil 18 Donkin, Stephen 18 Kannan, Subramaniam Senthamarai 18 Mazorchuk, Volodymyr 16 Green, Richard M. 16 Humphreys, James E. 16 Roichman, Yuval 15 Andersen, Henning Haahr 15 Borovik, Alexandre V. 15 Farnsteiner, Rolf 15 Marberg, Eric 14 Chastkofsky, Leonard 14 de Graaf, Willem Adriaan 13 Bunina, Elena Igor’evna 13 Coulembier, Kevin 13 Guralnick, Robert Michael 13 Hohlweg, Christophe 13 Reiner, Victor 13 Stroppel, Catharina H. 12 Azam, Saeid 12 Billey, Sara C. 12 Boe, Brian Douglas 12 Marietti, Mario 12 Pillen, Cornelius 12 Premet, Alexander A. 12 Renner, Lex E. 12 Shu, Bin 12 Singer, Michael F. 12 Stembridge, John R. 12 Tiep Pham Huu 12 Williamson, Geordie 12 Zhao, Kaiming 11 Bendel, Christopher P. 11 Chari, Vyjayanthi 11 Dyer, Matthew J. 11 Hultman, Axel 11 Malle, Gunter 11 Papi, Paolo 11 Sentinelli, Paolo 11 Shi, Jianyi 11 Testerman, Donna M. 11 Zalesski, Alexandre Efimovich 10 Khare, Apoorva 10 Larsen, Michael Jeffrey 10 Reading, Nathan 10 Vavilov, Nikolaĭ Aleksandrovich 10 Wang, Dengyin 9 Adin, Ron M. 9 Benkart, Georgia M. 9 Carnovale, Giovanna 9 Caselli, Fabrizio 9 Chen, Zhengxin 9 Elduque, Alberto 9 Hare, Kathryn E. 9 Helminck, Aloysius G. 9 Hosaka, Tetsuya 9 Huang, Wenxue 9 Lin, Zongzhu 9 McNinch, George J. 9 Navarro, Gabriel 9 Parshall, Brian J. 9 Proctor, Robert A. 9 Snow, Dennis M. 9 Sobaje, Paul 9 Terwilliger, Paul M. 8 Biagioli, Riccardo 8 Donnelly, Robert G. 8 Douglas, Andrew S. 8 Draper, Cristina 8 Eswara Rao, Senapathi 8 Jantzen, Jens Carsten 8 Lam, Thomas F. 8 Li, Haisheng 8 Musson, Ian M. 8 Navarro, Rosa María 8 Occhetta, Gianluca 8 Panyushev, Dmitri Ivanovich 8 Repka, Joe 8 Solá-Conde, Luis-Eduardo 7 Altınel, Tuna 7 Andruskiewitsch, Nicolás 7 Athanasiadis, Christos A. 7 Burness, Timothy C. 7 Cellini, Paola 7 Dechant, Pierre-Philippe 7 Deckhart, Robert W. 7 Doty, Stephen R. 7 Elias, Benjamin 7 Guillemin, Victor W. 7 Hrivnák, Jiří 7 Hu, Jun 7 Kaneda, Masaharu 7 Komori, Yasushi 7 Mühlherr, Bernhard Matthias 7 Pilaud, Vincent 7 Postnikov, Alexander 7 Precup, Martha E. ...and 3,724 more Authors
all top 5

### Cited in 368 Serials

 610 Journal of Algebra 207 Communications in Algebra 180 Transactions of the American Mathematical Society 170 Advances in Mathematics 141 Journal of Pure and Applied Algebra 101 Linear Algebra and its Applications 95 Proceedings of the American Mathematical Society 92 Mathematische Zeitschrift 78 Journal of Algebraic Combinatorics 64 Journal of Combinatorial Theory. Series A 63 Communications in Mathematical Physics 56 Inventiones Mathematicae 56 Transformation Groups 54 Annales de l’Institut Fourier 53 Mathematische Annalen 50 Duke Mathematical Journal 49 Representation Theory 46 Israel Journal of Mathematics 45 Journal of Mathematical Physics 43 Advances in Applied Mathematics 42 European Journal of Combinatorics 42 Algebras and Representation Theory 36 Discrete Mathematics 32 Nuclear Physics. B 31 Selecta Mathematica. New Series 29 Compositio Mathematica 29 Journal of Mathematical Sciences (New York) 28 Journal of Geometry and Physics 25 Linear and Multilinear Algebra 24 Geometriae Dedicata 24 Manuscripta Mathematica 23 Journal of Functional Analysis 23 Journal of Lie Theory 22 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 22 Journal of Algebra and its Applications 21 Journal of Number Theory 20 Archiv der Mathematik 20 Memoirs of the American Mathematical Society 20 Journal of the American Mathematical Society 19 The Electronic Journal of Combinatorics 18 Mathematical Proceedings of the Cambridge Philosophical Society 18 Indagationes Mathematicae. New Series 18 Journal of High Energy Physics 17 Letters in Mathematical Physics 17 Journal of Symbolic Computation 16 Siberian Mathematical Journal 16 Tôhoku Mathematical Journal. Second Series 16 Annals of Combinatorics 16 Journal of the European Mathematical Society (JEMS) 14 Differential Geometry and its Applications 14 Comptes Rendus. Mathématique. Académie des Sciences, Paris 13 Journal of Differential Equations 13 Annals of Mathematics. Second Series 12 Topology and its Applications 12 Acta Applicandae Mathematicae 12 Discrete & Computational Geometry 12 Bulletin of the American Mathematical Society. New Series 12 St. Petersburg Mathematical Journal 11 Proceedings of the Japan Academy. Series A 11 Publications of the Research Institute for Mathematical Sciences, Kyoto University 11 International Journal of Algebra and Computation 11 Journal of Group Theory 11 Acta Mathematica Sinica. English Series 11 Journal of the Australian Mathematical Society 11 Algebraic Combinatorics 10 Bulletin of the Australian Mathematical Society 10 Mathematical Notes 10 Algebra and Logic 10 Journal für die Reine und Angewandte Mathematik 10 Journal of Soviet Mathematics 10 International Journal of Mathematics 10 Proceedings of the Indian Academy of Sciences. Mathematical Sciences 10 Communications in Contemporary Mathematics 10 Journal of Nonlinear Mathematical Physics 10 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 9 Semigroup Forum 9 Experimental Mathematics 9 Séminaire Lotharingien de Combinatoire 9 Science China. Mathematics 8 Reports on Mathematical Physics 8 Mathematics of Computation 8 Canadian Journal of Mathematics 8 Geometric and Functional Analysis. GAFA 8 Annals of Physics 8 Expositiones Mathematicae 8 Central European Journal of Mathematics 7 Journal of Mathematical Analysis and Applications 7 Glasgow Mathematical Journal 7 Nagoya Mathematical Journal 7 Results in Mathematics 7 Annals of Global Analysis and Geometry 7 Forum Mathematicum 7 Advances in Applied Clifford Algebras 7 Bulletin des Sciences Mathématiques 7 The Ramanujan Journal 7 Algebraic & Geometric Topology 7 Journal of the Institute of Mathematics of Jussieu 6 Discrete Applied Mathematics 6 Physics Letters. A 6 Rocky Mountain Journal of Mathematics ...and 268 more Serials
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### Cited in 60 Fields

 1,695 Group theory and generalizations (20-XX) 1,304 Nonassociative rings and algebras (17-XX) 688 Algebraic geometry (14-XX) 588 Combinatorics (05-XX) 456 Topological groups, Lie groups (22-XX) 378 Associative rings and algebras (16-XX) 228 Number theory (11-XX) 216 Quantum theory (81-XX) 199 Differential geometry (53-XX) 165 Linear and multilinear algebra; matrix theory (15-XX) 141 Manifolds and cell complexes (57-XX) 138 Convex and discrete geometry (52-XX) 123 Commutative algebra (13-XX) 123 Dynamical systems and ergodic theory (37-XX) 120 Order, lattices, ordered algebraic structures (06-XX) 104 Several complex variables and analytic spaces (32-XX) 99 Special functions (33-XX) 93 Category theory; homological algebra (18-XX) 90 Geometry (51-XX) 78 Global analysis, analysis on manifolds (58-XX) 73 Algebraic topology (55-XX) 59 Abstract harmonic analysis (43-XX) 55 Computer science (68-XX) 54 Field theory and polynomials (12-XX) 52 Ordinary differential equations (34-XX) 46 Probability theory and stochastic processes (60-XX) 42 Partial differential equations (35-XX) 38 Functional analysis (46-XX) 36 Statistical mechanics, structure of matter (82-XX) 35 Mathematical logic and foundations (03-XX) 33 $$K$$-theory (19-XX) 26 Mechanics of particles and systems (70-XX) 25 Functions of a complex variable (30-XX) 25 Operator theory (47-XX) 24 Relativity and gravitational theory (83-XX) 21 Harmonic analysis on Euclidean spaces (42-XX) 18 Information and communication theory, circuits (94-XX) 17 Numerical analysis (65-XX) 16 Systems theory; control (93-XX) 15 Biology and other natural sciences (92-XX) 13 Measure and integration (28-XX) 11 Potential theory (31-XX) 10 Difference and functional equations (39-XX) 9 General algebraic systems (08-XX) 8 Integral transforms, operational calculus (44-XX) 6 Real functions (26-XX) 6 Approximations and expansions (41-XX) 6 Operations research, mathematical programming (90-XX) 5 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 4 Calculus of variations and optimal control; optimization (49-XX) 3 General topology (54-XX) 3 Statistics (62-XX) 3 Mechanics of deformable solids (74-XX) 2 Fluid mechanics (76-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 Optics, electromagnetic theory (78-XX) 1 Classical thermodynamics, heat transfer (80-XX)

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