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Results tagged with gr.group-theory
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user 22846
Questions about the branch of algebra that deals with groups.
7
votes
Accepted
Double covers of the orthogonal groups
Sorry for editing this answer multiple times. However, as I managed to get the answer wrong I feel obliged to improve this answer and provide a few more details. I've broken this up into several parts …
- 2,902
3
votes
Accepted
The irreducible character of $2.L_2(p)$ where p is a prime
OK, so if I am not mistaken the non-split extension of $L_2(p)$ should simply be $SL_2(p)$. You are now asking whether $SL_2(p)$ has a character of degree $(p-1)/2$ or $(p+1)2$ when $p \neq 2$. Indeed …
- 2,902
5
votes
Accepted
Sylow $p$-subgroup of GL
Steinberg's "Lecture Notes on Chevalley Groups" the Corollary of Lemma 54 on page 132. There is possibly a more modern reference.
EDIT: Sorry the reference to Steinberg is not sufficient as he does n …
- 2,902
1
vote
Regular elements in the torus of a group of Lie type
This is an old question now but I had cause to look at it recently. I thought it was worthwhile pointing out that Carter's proof about the existence of nondegenerate maximal tori in Proposition 3.6.6 …
- 2,902
7
votes
Accepted
Unipotent orbit in adjoint group over finite field
That's not what they're claiming and your statement is not true. Your claim is that every unipotent element is rational. However Lemma 5.6 of this article by Tiep and Zalesskii provides a counter exam …
- 2,902
3
votes
1
answer
1k
views
Richardson Classes and the Bala Carter Theorem
I am interested in trying to understand the following problem. Let $G$ be a connected simple algebraic group of type $D_n$, (with $n\geqslant 4$ even), defined over an algebraically closed field of od …
- 2,902
13
votes
Accepted
Analogy between product of conjugacy classes and irreps: is there analog of Thompson conject...
In the following article
Heide, Gerhard; Saxl, Jan; Tiep, Pham Huu; Zalesski, Alexandre E.
Conjugacy action, induced representations and the Steinberg square for simple groups of Lie type. Proc. …
- 2,902
31
votes
How do you *state* the Classification of finite simple groups?
I can't answer your general question but I can answer your side question. Almost all of the groups of Lie type are constructed as follows. You take a simple algebraic group $G$ defined over an algebra …
- 2,902
6
votes
Accepted
For a Weyl group, what is the connection between its exponents and lengths of its elements?
I would leave this as a comment but I don't appear to have enough reputation points for that. Just to add to Philippe's answer that you will also find this as Theorem 10.2.3 in Carter's "Simple Groups …
- 2,902
7
votes
How can classifying irreducible representations be a "wild" problem?
Well, to understand how this problem is wild it may be useful to contrast it with the situation of finite reductive groups where we do have a classification statement. The first part of this post cons …
- 2,902