0
$\begingroup$

Let $G$ be the multiplicative group of $n\times n$ invertible matrices over the finite field $\mathbb{F}_2$ of two elements. Consider the representation $\sigma(M):e_x\mapsto e_{Mx}$ acting on the space $V=\mathbb{C}\{x:x\in\mathbb{F}_2^n\}$.

Consider the subgroup $H$ of matrices which can be written in block diagonal form $\mathrm{diag}(1,N)$ where $N$ is an $(n-1)\times(n-1)$ invertible matrix.

I am interested in analyzing the irreps $(\rho,W)$ of $H$, the irrep content of the tensor product of irreps, and the decomposition of the induced representation $\mathrm{Ind}_H^G\rho$ into the irreps of $G$. My basic knowledge about representation theory comes from Serre which does not seem to have discussion about this finite group. But I think this should be a well-studied problem. It would be great if you could give me some reference (or at least some keywords) about this.

$\endgroup$

1 Answer 1

1
$\begingroup$

Question: "My basic knowledge about representation theory comes from Serre which does not seem to have discussion about this finite group. But I think this should be a well-studied problem. It would be great if you could give me some reference (or at least some keywords) about this."

Answer: "Representation Theory of Finite Groups: An Introductory Approach" - Benjamin Steinberg

$\endgroup$

You must log in to answer this question.

Not the answer you're looking for? Browse other questions tagged .