Algebras and Representation Theory

, Volume 13, Issue 5, pp 511–519

Remarks on the McKay Conjecture

Authors

    • Department of MathematicsUniversity of California at Santa Cruz
Open AccessArticle

DOI: 10.1007/s10468-009-9132-y

Cite this article as:
Mason, G. Algebr Represent Theor (2010) 13: 511. doi:10.1007/s10468-009-9132-y

Abstract

The McKay Conjecture (MC) asserts the existence of a bijection between the (inequivalent) complex irreducible representations of degree coprime to p (p a prime) of a finite group G and those of the subgroup N, the normalizer of Sylow p-subgroup. In this paper we observe that MC implies the existence of analogous bijections involving various pairs of algebras, including certain crossed products, and that MC is equivalent to the analogous statement for (twisted) quantum doubles. Using standard conjectures in orbifold conformal field theory, MC is equivalent to parallel statements about holomorphic orbifolds V G , V N . There is a uniform formulation of MC covering these different situations which involves quantum dimensions of objects in pairs of ribbon fusion categories.

Keywords

McKay correspondence Quantum double

Mathematics Subject Classification (2000)

20C05

Copyright information

© The Author(s) 2009