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Jim Humphreys

U. Massachusetts, Amherst

http://www.math.umass.edu/~jeh/

More-or-less retired professor at UMass Amherst. Basically an algebraist with interests in Lie theory, specifically representation theory and related algebraic geometry.

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Top Questions
60 votes

Origin of terms “flag”, “flag manifold”, “flag variety”?

ag.algebraic-geometry lie-groups ho.history-overview terminology flag-varieties asked Mar 13 '11 at 15:02
mathoverflow.net

59 votes

What are “classical groups”?

gr.group-theory reference-request algebraic-groups asked Dec 28 '10 at 23:27
mathoverflow.net

48 votes

Is Galois theory necessary (in a basic graduate algebra course)?

galois-theory teaching soft-question asked Aug 1 '10 at 17:11
mathoverflow.net

44 votes

What role does the “dual Coxeter number” play in Lie theory (and should it be called the “Kac number”)?

lie-algebras rt.representation-theory names asked May 22 '10 at 17:52
mathoverflow.net

38 votes

Implications of non-negativity of coefficients of arbitrary Kazhdan-Lusztig polynomials?

rt.representation-theory co.combinatorics lie-algebras coxeter-groups kazhdan-lusztig asked Nov 18 '12 at 0:35
mathoverflow.net

36 votes

Definition of “finite group of Lie type”?

gr.group-theory algebraic-groups finite-groups asked Jul 16 '13 at 15:13
mathoverflow.net

31 votes

Is there any need to study Coxeter systems (W,S) with S infinite?

gr.group-theory coxeter-groups asked Jan 31 '13 at 0:05
mathoverflow.net

29 votes

Greatly expanded new edition of a Bourbaki chapter on algebra?

ra.rings-and-algebras soft-question books bourbaki asked Jan 13 '16 at 14:51
mathoverflow.net

26 votes

Follow-up to Steinberg's problem (12) in his 1966 ICM talk?

reference-request gr.group-theory lie-algebras algebraic-groups asked Jul 18 '16 at 20:24
mathoverflow.net

25 votes

What was Casimir's precise role in describing the center of the universal enveloping algebra of a semisimple Lie algebra?

lie-algebras rt.representation-theory mp.mathematical-physics ho.history-overview asked Oct 5 '10 at 13:40
mathoverflow.net

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Top Answers
72
Motivating the Casimir element
mathoverflow.net

45
Books you would like to read (if somebody would just write them…)
mathoverflow.net

43
Fraktur symbols for Lie algebras
mathoverflow.net

37
What is significant about the half-sum of positive roots?
mathoverflow.net

36
Fields of mathematics that were dormant for a long time until someone revitalized them
mathoverflow.net

36
Pseudonyms of famous mathematicians
mathoverflow.net

34
Rep Theory Consequences of Bott--Weil--Borel
mathoverflow.net

28
Facts from algebraic geometry that are useful to non-algebraic geometers
mathoverflow.net

28
Why aren't representations of monoids studied so much?
mathoverflow.net

27
About unpublished lecture notes of Philip Hall
mathoverflow.net

24
How might M.C. Escher have designed his patterns?
mathoverflow.net

23
Isomorphic general linear groups implies isomorphic fields?
mathoverflow.net

22
Should I become a Mathscinet reviewer?
mathoverflow.net

21
What to do now that Lusztig's and James' conjectures have been shown to be false?
mathoverflow.net

21
Is there a Morse theory proof of the Bruhat decomposition?
mathoverflow.net

20
Small-index subgroups of SL(3,Z)
mathoverflow.net

20
Never appeared forthcoming papers
mathoverflow.net

20
Why are affine Lie algebras called affine?
mathoverflow.net

19
Why are $S$-arithmetic groups interesting?
mathoverflow.net

19
Cohomology of Flag Varieties
mathoverflow.net

18
Why are they called Specht Modules?
mathoverflow.net

18
Complex root systems
mathoverflow.net

18
Why the BGG category O?
mathoverflow.net

18
When and why did the postdoctoral position originate?
mathoverflow.net

17
Representation theory of the general linear group over a finite prime field
mathoverflow.net

17
Weyl group actions on 0-weight spaces
mathoverflow.net

16
What is modular representation theory for groups good for?
mathoverflow.net

16
Algebraic Groups in Characteristic p
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16
Abstract Jordan Decomposition different from usual Jordan Decomposition
mathoverflow.net

16
Do semisimple algebraic groups always have faithful irreducible representations?
mathoverflow.net

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