Remarks on the McKay Conjecture
| dc.creator | Mason, Geoffrey | |
| dc.date | 2008-07-22 | |
| dc.date.accessioned | 2026-07-07T09:52:09Z | |
| dc.date.available | 2026-07-07T09:52:09Z | |
| dc.description | 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 \emph{equivalent} to the analogous statement for (twisted) quantum doubles. Using standard conjectures in orbifold conformal field theory, MC is \emph{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. | |
| dc.identifier | https://arxiv.org/abs/0807.3546 | |
| dc.identifier | http://arxiv.org/abs/0807.3546 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/165494 | |
| dc.subject | Representation Theory | |
| dc.subject | 20C05 | |
| dc.title | Remarks on the McKay Conjecture | |
| dc.type | text |