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Jim Humphreys

U. Massachusetts, Amherst

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

Jim Humphreys (1939-2020)

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
74 votes

What are "classical groups"?

gr.group-theory reference-request algebraic-groups asked Dec 28, 2010 at 23:27
mathoverflow.net

66 votes

Origin of terms "flag", "flag manifold", "flag variety"?

ag.algebraic-geometry lie-groups ho.history-overview terminology flag-varieties asked Mar 13, 2011 at 15:02
mathoverflow.net

53 votes

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

galois-theory teaching soft-question asked Aug 1, 2010 at 17:11
mathoverflow.net

50 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, 2010 at 17:52
mathoverflow.net

49 votes

Definition of "finite group of Lie type"?

gr.group-theory algebraic-groups finite-groups asked Jul 16, 2013 at 15:13
mathoverflow.net

41 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, 2012 at 0:35
mathoverflow.net

35 votes

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

gr.group-theory coxeter-groups asked Jan 31, 2013 at 0:05
mathoverflow.net

32 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, 2010 at 13:40
mathoverflow.net

30 votes

Greatly expanded new edition of a Bourbaki chapter on algebra?

ra.rings-and-algebras soft-question books bourbaki asked Jan 13, 2016 at 14:51
mathoverflow.net

30 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, 2016 at 20:24
mathoverflow.net

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Top Answers
86
Motivating the Casimir element
mathoverflow.net

53
Books you would like to read (if somebody would just write them…)
mathoverflow.net

49
Fraktur symbols for Lie algebras
mathoverflow.net

47
What is significant about the half-sum of positive roots?
mathoverflow.net

46
Fields of mathematics that were dormant for a long time until someone revitalized them
mathoverflow.net

40
Rep Theory Consequences of Bott--Weil--Borel
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39
Pseudonyms of famous mathematicians
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31
How might M.C. Escher have designed his patterns?
mathoverflow.net

30
Facts from algebraic geometry that are useful to non-algebraic geometers
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29
Why aren't representations of monoids studied so much?
mathoverflow.net

28
About unpublished lecture notes of Philip Hall
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27
Why are affine Lie algebras called affine?
mathoverflow.net

25
What to do now that Lusztig's and James' conjectures have been shown to be false?
mathoverflow.net

24
Should I become a Mathscinet reviewer?
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24
Lie algebras of algebraic groups
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23
Isomorphic general linear groups implies isomorphic fields?
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22
Is there a Morse theory proof of the Bruhat decomposition?
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22
Cohomology of Flag Varieties
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22
On the full reducibility of representations of reductive Lie algebras
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21
Why the BGG category O?
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20
Small-index subgroups of SL(3,Z)
mathoverflow.net

20
finding highest weight of dual of a representation of a semisimple lie algebra
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20
Why are $S$-arithmetic groups interesting?
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20
Never appeared forthcoming papers
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20
What is modular representation theory for groups good for?
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19
Weyl group actions on 0-weight spaces
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19
Complex root systems
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19
Why are they called Specht Modules?
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18
Decompose tensor product of type $G_2$ Lie algebras.
mathoverflow.net

18
Representation theory of the general linear group over a finite prime field
mathoverflow.net

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