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2
votes
1answer
72 views

Stabilizer of a nonsingular vector in a quadratic space (char (k)=2)

suppose that $k$ is a finite field of characteristic 2 and $(V,q)$ a quadratic space, i.e., $V$ is a $k$-vector space and $q:V\to k$ quadratic form. Suppose that $\dim(V)\geq 4$ and that $q$ is ...
2
votes
1answer
166 views

question about projective special unitary group

Let $q$ be odd, $G=PSU_n(q)$ (Projective Special Unitary group) and $H=PSU_{n-1}(q)$. Is it always true that $H$ is a subgroup of $G\ ?$
2
votes
1answer
99 views

Hilbert's Finiteness Theorem for connected semisimple Lie groups in Weyl's “Classical Groups”

First of all, sorry for using this account. Somehow I can't login to my previous one anymore and am thus using the account associated to my MSE one. Also, I already asked the question on MSE, but ...
3
votes
0answers
166 views

multidimensional rotation terminology

Given an element $g$ of the orthogonal group $O(n)$, is there a name for the subspace of $R^n$ that's fixed by $g$, and a name for the orthogonal complement of this space? (The latter is what I ...
18
votes
1answer
868 views

Existance of certain almost invariant functions related to amenability and piece-wise transformations

We would like very much to know the answer to the following question: Let $\|\cdot\|$ be any norm on $\mathbb{Z}^d$ and let $W(\mathbb{Z}^d)$ be the group of all bijections of $\mathbb{Z}^d$ such ...
7
votes
2answers
1k views

Connectedness of the linear algebraic group SO_n

I apologize in advance if my question is too elementary for MO. It is a well known fact that the linear algebraic group $G = \mathsf{SO}_n$ is connected, and there exist a few different proofs of ...
1
vote
0answers
229 views

Totally singular subspaces in orthogonal vector spaces

This is for all that are interested in classical groups and their representations. We are investigating the following situation: Let $V$ be $d$-dimensional $k$-vector space (where $k$ is a finite ...
8
votes
0answers
294 views

What is the “positive part” of the unit ball in $M_n(R)$ ?

In ${\bf M}_n(\mathbb R)$, let us consider the usual operator norm $$\|A\|=\sup\frac{\|Ax\|}{\|x\|},$$ where $\|x\|$ is the Euclidian norm. The closed unit ball $B$ is the set of contractions (in the ...
4
votes
1answer
430 views

Symplectic groups Sp_{2m}(2) as 2-transitive permutation (i.e. Galois) groups

Hello, I am looking for information about the symplectic groups $Sp_{2m}(2)$ as permutation group acting on quadratic forms. Consider the block matrices ...
13
votes
2answers
1k views

Alternate and symmetric matrices

Greetings to all ! Let me first confess that this question was mentionned to me by Bernard Dacorogna, who doesn't sail on MO. Let $A\in M_{2n}(k)$ be an alternate matrix. Say that $A$ is ...
12
votes
3answers
1k views

What is the subgroup generated by involutions?

I was recently taking some notes on the Cartan-Dieudonné theorem: if $(V,q)$ is a nondegenerate quadratic space of finite dimension $n$ over a field of characteristic not $2$, then every element of ...