31,162 reputation
363137
bio website math.umass.edu/~jeh
location U. Massachusetts, Amherst
age 75
visits member for 4 years, 11 months
seen 7 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.

1d
comment Tensor products of Weyl modules in positive characteristic
@Konstantin: In 2014 I got around to writing up some informal notes on "Weyl modules" (and their duals), which might clarify the transition in terminology which Chuck commented on. See people.math.umass.edu/~jeh/pub/weyl.pdf
1d
awarded  Nice Answer
2d
comment What Is The Minimal Monomial of the Symmetric Group?
The question looks quite nontrivial, but is there some specific motivation for it?
Jan
24
comment the number of indecomposable modules of finite groups over finite fields of a fixed dimension
As Derek points out, the formulation is not quite clear. Usually a conjecture as general as this is based on some computational evidence for typical small groups, so it's relevant to ask what examples you've studied. (Also, more tags such as 'finite-groups' and 'rt.representation-theory' are needed.)
Jan
23
comment Bruhat order in homogeneous spaces
Too many questions here! Also, the first one has an obvious answer in rank 1, where the simple root is twice the corresponding fundamental weight. (See the Bourbaki tables for explicit results on other types.)
Jan
23
comment Special linear groups over function fields
There is quite a bit of related literature. The English translation of Serre's monograph is listed here: ams.org/mathscinet-getitem?mr=1954121, but there are also lots of papers such as ams.org/mathscinet-getitem?mr=0114866 and ams.org/mathscinet-getitem?mr=1177335
Jan
23
comment Subquotients in the Verma filtration on Verma modules
@Allen: There are several fine points to add if you want a real algorithm, but my edited answer is already getting too long.
Jan
22
comment Elements of order 3 normalizing no non-identity 2-subgroups in Almost Simple Groups
@Geoff: Maybe add a tag such as 'finite-groups'. I suppose the classification of simple groups is needed here?
Jan
22
revised Subquotients in the Verma filtration on Verma modules
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Jan
21
comment Subquotients in the Verma filtration on Verma modules
@Allen: Yes, the lower rank type A examples are often misleadingly well-behaved. Best to be skeptical.
Jan
20
revised What is modular representation theory for groups good for?
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Jan
20
answered What is modular representation theory for groups good for?
Jan
20
comment Canonical basis of quantum groups
Note that Lusztig's paper is freely available online and has some discussion of low rank examples in 3.4 including this rank 1 case: ams.org/mathscinet-getitem?mr=1035415 (see also the answer to your June question on canonical bases).
Jan
20
comment PBW basis and canonical basis
This is illustrated in Lusztig's original J.A.M.S. (1990) paper in low rank examples. Also, some computational methods are given in papers by W.A. deGraaf: ams.org/mathscinet-getitem?mr=1959260, ams.org/mathscinet-getitem?mr=1987542
Jan
20
comment What is modular representation theory for groups good for?
This is an extremely open-ended question, which may or may not be suitable for this forum but doesn't have a single answer. Should it be community-wiki?
Jan
19
comment Computing maximal ideals of a Lie algebra
It might still be helpful to ask him directly by email (I think he is now at the University of Trento in Italy), since he is quite experienced with Lie algebra algorithms.
Jan
19
revised Convention about “long” roots for simple Lie algebras of types ADE?
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Jan
19
comment Computing maximal ideals of a Lie algebra
Have you looked at W.A. de Graaf's book ams.org/mathscinet-getitem?mr=1743970 (or his papers)?
Jan
19
revised Convention about “long” roots for simple Lie algebras of types ADE?
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Jan
16
comment Number of Irreducible Representations of $U_q(n)$ of Dimension $n$?
@Ajabnaz: One other comment is that $N$ in your heading should be $n$.