33,041 reputation
371147
bio website math.umass.edu/~jeh
location U. Massachusetts, Amherst
age 75
visits member for 5 years, 6 months
seen 1 hour ago
More-or-less retired professor at UMass Amherst. Basically an algebraist with interests in Lie theory, specifically representation theory and related algebraic geometry.

1d
comment Form of elements of a Lie algebra
@Bruce: Probably it's helpful to include more details about the book ams.org/mathscinet-getitem?mr=1231799, along with the later short expository article ams.org/mathscinet-getitem?mr=2035110
Aug
27
awarded  Nice Answer
Aug
26
awarded  Nice Answer
Aug
21
comment Any representation is a sub representation of direct sum of regular representation
As abx and David point out, this is a basic (early) lemma in the Chevalley development of affine algebraic groups. It's found in textbooks by Borel et al., and generalizes well to affine group schemes as Scott Carnahan indicates. The traditional language involves "representative functions" as developed by Chevalley, Hochschild, and others. (The notes of Steinberg's Tata lectures were written up by Deodhar, then a student there, but could have used some editing.)
Aug
20
comment Casselman-Shalika formula for split reductive groups
This does seem to be a helpful reference (which I've corrected to get the link right).
Aug
20
revised Casselman-Shalika formula for split reductive groups
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Aug
16
awarded  Popular Question
Aug
14
comment Classification of finite group schemes over a field
As Jason points out, there is a big difference depending on the characteristic of the field. In prime characteristic there are also Frobenius kernels, etc.
Aug
13
comment Coxeter Subgroups of Coxeter Groups
Be careful about the formulation: being a "Coxeter group" requires fixing a set of involutive generators. However, a finite symmetric group $S_n$ will typically contain a lot of smaller Coxeter groups whose generators have nothing to do with those of $S_n$ itself, since every finite group has some embedding in a symmetric group. In another direction, a subgroup of a Coxeter group generated by a finite set of "reflections" (conjugates of the given generators) will be a Coxeter group relative to this new set of involutions (Deodhar, Dyer). Many possibilities.
Aug
13
comment Role of nontrivial component groups in Springer Correspondence?
@Dror: Yes, I should have specified that $G$ is semisimple of adjoint type as is usually done in the literature on Springer correspondence, to avoid such cases. I've edited appropriately. Thanks for pointing this out.
Aug
13
revised Role of nontrivial component groups in Springer Correspondence?
added 51 characters in body
Aug
13
revised Normalized invariant form on a Kac-Moody Algebra
edited tags
Aug
13
answered Normalized invariant form on a Kac-Moody Algebra
Aug
12
awarded  Necromancer
Aug
12
comment Are the orders of the generators of a group and the product of pairs of thereof enough for this group to be isomorphic to a Coxeter group?
@Geoff: Your expanded answer is more helpful, though I was still wondering how to specify a smallest possible $G$ of the type specified which couldn't have the structure of a Coxeter group. Is there a smallest such simple group one can point to?
Aug
12
answered Are the orders of the generators of a group and the product of pairs of thereof enough for this group to be isomorphic to a Coxeter group?
Aug
12
revised Are the orders of the generators of a group and the product of pairs of thereof enough for this group to be isomorphic to a Coxeter group?
added 10 characters in body; edited tags; edited title
Aug
11
revised Bruhat decomposition for reductive groups in characteristic zero?
deleted 18 characters in body
Aug
11
comment Bruhat decomposition for reductive groups in characteristic zero?
@ L Spice: No, that was just too hurriedly written. Will edit. Thanks.
Aug
6
comment Generalization of a theorem of Steinberg
@Nick: Yes, that's the paper by Matt Douglass. The Lehrer paper has open access if you follow the article link given and click on PDF at the lower right. (MathSciNet access shouldn't be needed for the two links I gave.)