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15 January 2002 Twisted vertex representations via spin groups and the McKay correspondence
Igor B. Frenkel, Naihuan Jing, Weiqiang Wang
Duke Math. J. 111(1): 51-96 (15 January 2002). DOI: 10.1215/S0012-7094-02-11112-0

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 ${\rm SL}_2(\mathbb {C})$ with the McKay virtual character, our construction gives a group-theoretic realization of the basic representations of the twisted affine and twisted toroidal Lie algebras. When $\Gamma$ is an arbitrary finite group and the virtual character is trivial, our vertex operator construction yields the spin character tables for $\Gamma\wr \tilde {S}_n$.

Citation

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Igor B. Frenkel. Naihuan Jing. Weiqiang Wang. "Twisted vertex representations via spin groups and the McKay correspondence." Duke Math. J. 111 (1) 51 - 96, 15 January 2002. https://doi.org/10.1215/S0012-7094-02-11112-0

Information

Published: 15 January 2002
First available in Project Euclid: 18 June 2004

zbMATH: 1100.17502
MathSciNet: MR1876441
Digital Object Identifier: 10.1215/S0012-7094-02-11112-0

Subjects:
Primary: 17B69
Secondary: 05E05 , 20C25

Rights: Copyright © 2002 Duke University Press

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Vol.111 • No. 1 • 15 January 2002
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