A numerical invariant for linear representations of finite groups
Abstract
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 prove analogues of classical theorems of R. Brauer and O. Schilling about the Schur index, where the Schur index of a representation is replaced by its essential dimension. In the last section we show that essential dimension of representations can behave in rather unexpected ways in the modular setting.
Cite
@article{arxiv.1405.4037,
title = {A numerical invariant for linear representations of finite groups},
author = {Nikita A. Karpenko and Zinovy Reichstein},
journal= {arXiv preprint arXiv:1405.4037},
year = {2014}
}
Comments
24 pages. Corrected minor typos, added a section on essential dimension of modular representations