30,645 reputation
361134
bio website math.umass.edu/~jeh
location U. Massachusetts, Amherst
age 75
visits member for 4 years, 10 months
seen 53 mins ago
More-or-less retired professor at UMass Amherst. Basically an algebraist with interests in Lie theory, specifically representation theory and related algebraic geometry.

5h
revised Extension of an involutive automorphism
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answered Extension of an involutive automorphism
10h
comment Extension of an involutive automorphism
This may be a reasonable question, but you have to keep in mind that g' can be considerably smaller than g. Moreover, g' might have an involutive outer automorphism while g doesn't; so there might be a complicated mix of inner/outer here. I'm not optimistic about getting a useful criterion for an arbitrary pair (g,g').
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revised Subquotients in the Verma filtration on Verma modules
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2d
answered ULU Decomposition of a matrix
Dec
18
awarded  Nice Answer
Dec
17
comment automorphism of prime order for group of Lie type in
@Maryam: Note that your header is incomplete. Also, it might be helpful to indicate what your motivation for the question is.
Dec
17
comment Closure relations between Bruhat cells on the flag variety
The three authors (then in Moscow) also known as BGG were Joseph Bernstein together with his teacher Israel Gelfand and Gelfand's son Sergei. The paper is available online in Russian: mathnet.ru/php/…
Dec
17
comment A generalisation of the theorem of Maschke
Even though your answer comes a bit late, it's always useful to provide a reference like this for a classical result rather than just sketching a proof. No need to reinvent the wheel here.
Dec
16
comment Reductive Lie Groups and Complexification
If the Lie algebra is reductive, it must be the direct sum of a semisimple Lie algebra and its center = radical (one of Bourbaki's equivalent conditions). This is stronger than just having an abelian unipotent radical in the group $G$.
Dec
16
comment reference help indecomposable representations of SL(2,R)
Maybe "complete" is an overstatement, but in any case what Howe and Tan do is quite explicit.
Dec
16
comment reference help indecomposable representations of SL(2,R)
For the article in English by Soergel, try the list of publications on his homepage (where a postscript version is linked): home.mathematik.uni-freiburg.de/soergel/#Preprints
Dec
14
comment Central idempotents from characters in Frobenius algebras (generalizing Lusztig arXiv:math/0208154v2 §19)
@darij: Your question is impressively detailed (and long). I probably can't add anything useful to what has been said here, but it may be worth emphasizing the range of examples beyond group algebras of finite groups. The "symmetric" algebras defined by Brauer's student Nesbitt (here "symmetric Frobenius" algebras) include many but not all restricted enveloping algebras in prime characteristic, as well as related reduced enveloping algebras, Frobenius kernels, etc. (see for instance ams.org/mathscinet-getitem?mr=0485965).
Dec
13
comment Comparison of two Chevalley basis
I don't see what this has to do with Springer's work, since the ideas here originate with Chevalley, Borel-Tits, Iwahori-Matsumoto. The formulation needs a little editing; e.g., your $n(\alpha)$ should be $n(s_\alpha)$. It's not clear what "simply connected" contributes here, though it does imply $H$ is connected (Springer-Steinberg, 1963). Anyway, $W_H$ is generated by reflections $s_\alpha$ in $W$ with $\alpha$ running over some positive roots (not necessarily simple). I guess this is what complicates your comparison of sections.
Dec
13
comment Dihedral subgroups of $\mathrm{PSL}_2(\mathbb{F}_q)$
@Geoff: This looks helpful.
Dec
12
comment Dihedral subgroups of $\mathrm{PSL}_2(\mathbb{F}_q)$
@Geoff: This is a helpful concise summary. Is there any published source for this particular question? I was reluctant to go back as far as Dickson, but these are pretty well-studied groups.
Dec
12
comment Dihedral subgroups of $\mathrm{PSL}_2(\mathbb{F}_q)$
@M.B.: Minor edits. You may want to separate the cases $p=2$ and $p$ odd here. For odd $p$, your group has order $q(q−1)(q+1)/2$, where $q−1$ is the order of the group of rational points of a split torus in $\mathrm{SL}(2,q)$ and $q+1$ is the order of the group of rational points of a torus which splits only over a quadratic extension, while $q$ is the order of a Sylow $p$-subgroup. The subgroup structure is not too mysterious, but your specific question may not be answered directly in the literature
Dec
11
revised Dihedral subgroups of $\mathrm{PSL}_2(\mathbb{F}_q)$
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Dec
10
revised orders of maximal abelian subgroups
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Dec
10
comment Representation of GL(n, F_p) over F_p, for n small
@Gao: I wrote a fairly detailed survey Modular Representations of Finite Groups of Lie Type, which appeared in 2006 as London Math. Soc. Lecture Note Ser. 326 (Cambridge U. Press). Almost nothing there is original, but it includes some treatment of special cases including general linear groups. You might find the 460 references useful. (See also the revisions on my homepage.)