Twisted vertex representations via spin groups and the McKay correspondence

Details Twisted vertex representations via spin groups and the McKay correspondence Twisted vertex representations via spin groups and the McKay correspondence

2000-07-26

arxiv.org/abs/math/0007159v2

Duke Math. J. 111 (2002), 51-96

Mathematics

Quantum Algebra

45 pages

Scientific paper

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 $\Gamma\wr\widetilde{S}_n$ of $\Gamma$ and a double cover of the symmetric group $S_n$ for all $n$. When $\Gamma$ is a subgroup of $SL_2(\mathbb C)$ 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 $\Gamma\wr\widetilde{S}_n$.

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