27,992 reputation
353118
bio website math.umass.edu/~jeh
location U. Massachusetts, Amherst
age 74
visits member for 4 years, 1 month
seen 2 hours ago
More-or-less retired professor at UMass Amherst. Basically an algebraist with interests in Lie theory, specifically representation theory and related algebraic geometry.

2d
comment Bruhat order and Schubert cycles
P.S. I'm still not sure what you mean by "flag manifold" for an arbitrary semisimple Lie group without compact factors. In the mostly equivalent algebraic setting, what Borel and Tits do seems to be optimal but deals with some $G/P$ and its points over the field.
2d
answered Bruhat order and Schubert cycles
2d
comment Bruhat order and Schubert cycles
@Misha: You need to clarify the precise set-up you have in mind for a real semisimple Lie group. In the extreme cases where this group is compact (with flag variety/manifold $G/T$) or is split, the complex case adapts well. But in general, there may be no Borel subgroup over $\mathbb{R}$ to use in the construction, and the Weyl group relative to a minimal parabolic is only a relative version of the usual Weyl group. It gets complicated.
Apr
14
comment abstract simplicity results for anisotropic quasi-simple algebraic groups defined over a non-archimedean local field
The Borel-Tits theory doesn't address this kind of question, but instead develops general structure and classification theorems for isotropic groups. The anisotropic case is much more open-ended and depends essentially on the fields involved. For this you need to look instead at the extensive literature ranging from Dieudonne to G. Prasad and A. Rapinchuk, etc. The recent book by Conrad-Gabber-Prasad would help to provide the modern framework.
Apr
13
comment Tensor products of two irreducible representations of reductive groups and their inclusions
This reference to PRV's Theorem 2.1 eluded me at first, but it's definitely the most standard way to see that each irreducible summand of the smaller tensor product occurs at least as often in the larger one. It does take some work to translate things into their notation or Khare's. The proof doesn't seem to involve a "natural" or "canonical" embedding (however those terms are defined), but maybe there is a more conceptual method lurking in later work by Shrawan Kumar or others.
Apr
12
revised Tensor products of two irreducible representations of reductive groups and their inclusions
added 108 characters in body
Apr
12
answered Tensor products of two irreducible representations of reductive groups and their inclusions
Apr
12
comment Learning representation theory of real reductive lie groups
This is a natural question but not at all research-level. Aside from that, there is no single answer that would work for everyone, so community-wiki is appropriate. But did you try math.stackexchange.com/questions?
Apr
12
comment Is the big cell a principal open set?
@abx: The reference you include is most helpful, even though they limit their discussion for convenience to characteristic 0 (while pointing out the general case). Maybe it's helpful to add the source of the artcile: Algebraische Transformationsgruppen und Invariantentheorie, 63–75, DMV Sem., 13, Birkhäuser, Basel, 1989.
Apr
12
comment Is the big cell a principal open set?
@Jesko: It's worth emphasizing that the picture is basically the same for all (connected) reductive groups in all characteristics. The reference by Knop et al. to a 1976 Advances in Math. paper by Birger Iversen is most relevant, I think.
Apr
11
comment Connection between two theorems on character values?
Just a brief added comment from the current AMS webpage, the news that Sandy Green has recently died at age 88. See also the extensive biographical page at MacTutor www-groups.dcs.st-and.ac.uk/~history/Biographies/…
Apr
11
revised Connection between two theorems on character values?
added 185 characters in body
Apr
10
comment Looking for paper: Weil's original 1952 “Sur les formules explicites de la théorie des nombres premiers”
@TA Wong: I'd add to the reference abx gives one comment, that Weil adds more than a page of retrospective commentary on this paper in the section Commentaire at the end of volume 2. While "most" libraries might not have Weil's collected papers, it's the most natural place to look for this particular one.
Apr
8
awarded  Popular Question
Apr
7
asked Connection between two theorems on character values?
Apr
6
comment Decomposition of a representation of SU(N) into representations of SU(N-1)
It's useful to search Math Overflow for "branching rules", including the link mathoverflow.net/questions/148888/…
Apr
6
comment What is the intuition behind the definition of cuspidal representations?
It's a good idea to look at the discussion and references in the related post mathoverflow.net/questions/154490/…
Apr
4
comment Reduction of different RG lattices to kG modules
As Geoff points out, this kind of question has been raised previously: mathoverflow.net/questions/130022, though I was too lazy to search for it (and will remove my redundant answer here).
Apr
4
awarded  Fanatic
Apr
3
comment What's the status of Arthur's announced classification for GSp(4)?
Though I'm not a specialist in this area, I wonder if you've taken advantage of the citation trail in MathSciNet? This leads to many further papers. Aside from that, I certainly agree with David that it would be worth asking Jim Arthur himself for guidance. His expository article is reviewed here: MR2058604 (2005d:11074) Automorphic representations of GSp(4). Contributions to automorphic forms, geometry, and number theory, 65–81, Johns Hopkins Univ. Press, Baltimore, MD, 2004.