Twisted vertex representations via spin groups and the McKay correspondence

Abstract

We establish a twisted analog of our recent work on vertex representations and the McKay correspondence. For each finite group $\Gamma$ and a virtual character of $\Gamma$ we construct twisted vertex operators on the Fock space spanned by the super spin characters of the spin wreath products $\Gamma \wr {\tilde{S}}_n$ of $\Gamma$ and a double cover of the symmetric group $S_n$ for all $n$. When $\Gamma$ is a subgroup of $S{L}_2(\mathbb{C})$ with the McKay virtual character, our construction gives a group theoretic realization of the basic representations of the twisted affine and twisted toroidal algebras. When $\Gamma$ is an arbitrary finite group and the virtual character is trivial, our vertex operator construction yields the spin character tables for $\Gamma \wr {\tilde{S}}_n$.

45 pages

References in corpus (3)

• Vertex representations via finite groups and the McKay correspondence
• Quantum vertex representations via finite groups and the McKay correspondence
• New twisted quantum current algebras

Cited by in corpus (4)

• A general approach to Heisenberg categorification via wreath product algebras
• Twisted vertex representations and spin characters
• Twisted Heisenberg doubles
• Spin characters of generalized symmetric groups