karpenko at ualberta.ca, reichst at math.ubc.ca
Submission: 2014, May 15, revised: 2014, June 18
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.
2010 Mathematics Subject Classification: 14C25, 16K50, 20C05
Keywords and Phrases: Representations of finite groups, characters, Schur index, central simple algebras, essential dimension, Severi-Brauer varieties, Weil transfer, Chow groups and motives, canonical dimension and incompressibility
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