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Results tagged with rt.representation-theory
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user 36466
Linear representations of algebras and groups, Lie theory, associative algebras, multilinear algebra.
15
votes
Accepted
are irreducible representations with large fixed subspaces trivial?
Unless I have misread either your question or their result, Corollary 1.2 in "Average dimension of fixed point spaces with applications" by Bob Guralnick and Attila Mar\'oti includes a positive answer …
- 3,571
3
votes
Help identify this generalized sign of real representations
I think the answer to your second question is "no". Note first that by the M\"obius inversion formula (see for example Chapter 3 of Richard Stanley's ``Enumerative Combinatorics, Volume 1"), for any …
- 3,571
11
votes
Accepted
Effect on homology of decorating vertices of a simplicial complex
If I understand correctly, $w \in S_m$ acts by sending $(v,i)$ to $(v,w(i))$. If so, you are in the nice situation where the stabilizer of a face fixes every point in that face. So, for $w \in S_m$, …
- 3,571
8
votes
Accepted
Tensor products of permutation representations of symmetric groups.
Hi Dev,
It looks to me like a proof of this fact is given in the answer to Exercise 7.84(b) of Richard Stanley's Enumerative Combinatorics, volume 2, along with a reference to Example I.7.23(e), page …
- 3,571
16
votes
Accepted
Dimension of Specht Modules $S^\lambda$
The opposite is true. It is a result of D. Craven, settling a conjecture of A. Moreto, that given any $k$, for all large enough $n$, there are at least $k$ distinct irreducible representations of $S_ …
- 3,571
5
votes
Field with one element look at counting index-$n$ subgroups in terms of Homs to $S_n$, gener...
Thomas M\"uller has done a very careful and thorough study of problems of this type. While I don't know that the formula you write is a special case of Theorem 1 in his paper ``Enumerating Representa …
- 3,571
5
votes
Accepted
Is there a maximal subgroup of depth 3?
As Noah points out, you are looking for some (core-free) maximal subgroup $H<G$ such that $1_H^G$ has nonzero inner product with every irreducible character.
Say $G=L_2(p)$ with $p$ prime and $p \equ …
- 3,571