Weil representations of finite general linear groups and finite special linear groups

Linear Representations of Finite Groups

Finite p-groups with few non-linear irreducible character kernels

Abstract. In this paper, we classify all of the finite p-groups with at most three non linear irreducible character kernels.

Non-linear residually finite groups

We prove that groups 〈a, b, t | tat = a, tbt = b〉 are not linear provided k, l 6∈ {−1, 1}. As a consequence we obtain the first example of a non-linear residually finite 1related group.

Linear representations of soluble groups of finite Morley rank

Sufficient conditions are given for groups of finite Morley rank having non-trivial torsion-free nilpotent normal subgroups to have linear representations with small kernels. In particular, centreless connected soluble groups of finite Morley rank with torsion-free Fitting subgroups have faithful linear representations. On the way, using a notion of definable weight space, we prove that certain...

A Numerical Invariant for Linear Representations of Finite Groups

We study the notion of essential dimension for a linear representation of a finite group. In characteristic zero we relate it to the canonical dimension of certain products of Weil transfers of generalized Severi-Brauer varieties. We then proceed to compute the canonical dimension of a broad class of varieties of this type, extending earlier results of the first author. As a consequence, we pro...