bio  website  math.umass.edu/~jeh 

location  U. Massachusetts, Amherst  
age  74  
visits  member for  4 years, 5 months 
seen  14 hours ago  
stats  profile views  14,390 
Moreorless retired professor at UMass Amherst.
Basically an algebraist with interests in Lie theory,
specifically representation theory and related
algebraic geometry.
2d

comment 
References for crystal bases and Demazure modules in representation theory
This is really a broad question (and needs more tags such as rt.representationtheory and referencerequest). There are lots of sources but with different emphases. For instance, HongKang, Introduction to Quantum Groups and Crystal Bases, GSM 42, AMS, 2002. And a relevant book by Kumar, etc. 
Jul 19 
comment 
Calculation with weights of $E_6$
@Claudio: In your added paragraph, what do you mean by saying $\Gamma \subset W$? Some points are still a little out of focus, though what you are aiming at is probably OK. 
Jul 16 
revised 
Is the Duflo polynomial conjecture open?
edited body; edited tags 
Jul 16 
comment 
Is the Duflo polynomial conjecture open?
It would help to give one or two explicit references here. (And I corrected a typo.) 
Jul 15 
comment 
Springer Isomorphisms for Adjoint Simple Exceptional Groups
Maybe it works here and even in types $G_2, F_4$, though I'm a bit skeptical about getting this simple algorithm from such arbitrary choices of root ordering. Anyway, aside from type $A_n$ the isogeny class doesn't seem to affect anything; does "exceptional" matter? Note too that there are numerous "Springer isomorphisms", considered by McNinchTesterman: front.math.ucdavis.edu/0805.2574 
Jul 15 
comment 
Unipotent conjugacy classes
The question is a bit unfocused, since "unipotent" is not directly related to Lie group structure (instead it depends on the algebraic group structure, and the count of unipotent classes is then the same in all good characteristics). As Peter Crooks indicates, there is no "simple" formula even in the general or special linear groups. 
Jul 14 
comment 
Representations of orthogonal groups vs representations of reflection groups
You may be asking for too much in this broad formulation, since a finite reflection group might embed as a subgroup of many orthogonal groups. Aside from this, it would be helpful to specify the field here, or at least clarify whether you mean "real reflection group" (there being many more "complex reflection groups" to consider). 
Jul 12 
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What is natural about the wellknown bijection between conjugacy classes and irreps of a symmetric group?
@Alexander: Though it's not as direct a connection as you might want, there has been subtle work relating classes of a Weyl group $W$ (such as $S_n$) and nilpotent orbits of a corresponding Lie algebra (here parametrized by partitions of $n$). Springer theory then leads to irreducible representations of $W$. The fit is exact for $S_n$. References include R.W. Carter, G.B. Elkington, A note on the parametrization of conjugacy classes, J. Algebra 20 (1972) 350354; D. Kazhdan, G. Lusztig, Fixed point varieties on affine flag manifolds, Israel J. Math. 62 (1988),129168. 
Jul 12 
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Tensor products of two irreducible representations of reductive groups and their inclusions
My last paragraph is accurate, but I was simplifying the original formulation by replacing $\mu^*$ by $\mu$. Anyway, Victor's answer and the fuller version I got from Kumar extract the answers to (1) and (2) mainly from PRV. For (2) it's probably not strictly necessary to interpret the modules as global sections of line bundles, but for this version the best convention is to use $B^$ rather than $B$. Algebraic group people like Andersen and Jantzen write things this way. Mixing $B, B^$ gets confusing. 
Jul 11 
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Calculation with weights of $E_6$
@Claudio: Can you clarify your notation $A_2$? 
Jul 8 
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Quadratic Casimir of fundamental irreps of simplylaced Lie algebras
@Peter: If you send me an email, I can explain in a little more detail the idea coming from Freudenthal's method which seems to be crucial in your observation (but only casebycase so far): The underlying question is to relate the "support" of a simple root $\alpha_i$ in the set of all $N$ positive roots to the Coxeter number $h=2N/\ell$ when the corresponding fundamental weight $\varpi_i$ is minuscule. 
Jul 7 
revised 
Quadratic Casimir of fundamental irreps of simplylaced Lie algebras
added 418 characters in body 
Jul 3 
revised 
Quadratic Casimir of fundamental irreps of simplylaced Lie algebras
added 295 characters in body 
Jul 3 
accepted  Number of Richardson orbits in simple Lie algebras of types $E_n$? 
Jul 3 
comment 
Number of Richardson orbits in simple Lie algebras of types $E_n$?
Thanks. Your count of Richardson orbits for types $F_4$ and $E_n$ does seem consistent with Hirai. As you say, the literature on induced orbits is more comprehensive, though it still takes some work to see how many distinct Richardson orbits emerge from the larger list of conjugacy classes of Levi subalgebras. It surprises me that the results aren't made more explicit in the literature, but I'll look again at Elashvili's papers. 
Jul 2 
awarded  Inquisitive 
Jul 2 
awarded  Curious 
Jul 2 
revised 
Quadratic Casimir of fundamental irreps of simplylaced Lie algebras
deleted 1 character in body 
Jul 2 
answered  Quadratic Casimir of fundamental irreps of simplylaced Lie algebras 
Jul 1 
comment 
Quadratic Casimir of fundamental irreps of simplylaced Lie algebras
P.S. To be more specific, are you looking at just the fundamental weights corresponding to minuscule representations? (These have just a single orbit of weights under the Weyl group, but don't exist for some types including $E_8$.) 