Inner products of 2-representations
Category Theory
2012-08-27 v2 Algebraic Geometry
Representation Theory
Abstract
We define and calculate inner products of 2-representations. Along the way, we prove that the categorical trace Tr(-) of [Ganter and Kapranov, Representation and character theory in 2-categories, Sec. 3] is multiplicative with respect to various notions of categorical tensor product, and we identify the center of the category V^G of [loc. cit., Sec. 4.2]. We discuss applications, ranging from Schur's result about the number of projective representations to a formula for the Hochschild cohomology of a global quotient orbifold.
Keywords
Cite
@article{arxiv.1110.1711,
title = {Inner products of 2-representations},
author = {Nora Ganter},
journal= {arXiv preprint arXiv:1110.1711},
year = {2012}
}
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