Twisted vertex representations via spin groups and the McKay correspondence
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2000
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| _version_ | 1866929304135270400 |
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| author | Frenkel, Igor Jing, Naihuan Wang, Weiqiang |
| author_facet | Frenkel, Igor Jing, Naihuan Wang, Weiqiang |
| contents | We establish a twisted analog of our recent work on vertex representations and the McKay correspondence. For each finite group $Γ$ and a virtual character of $Γ$ we construct twisted vertex operators on the Fock space spanned by the super spin characters of the spin wreath products $Γ\wr\widetilde{S}_n$ of $Γ$ and a double cover of the symmetric group $S_n$ for all $n$. When $Γ$ 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 $Γ$ is an arbitrary finite group and the virtual character is trivial, our vertex operator construction yields the spin character tables for $Γ\wr\widetilde{S}_n$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_math_0007159 |
| institution | arXiv |
| publishDate | 2000 |
| record_format | arxiv |
| spellingShingle | Twisted vertex representations via spin groups and the McKay correspondence Frenkel, Igor Jing, Naihuan Wang, Weiqiang Quantum Algebra Representation Theory 17B, 20C We establish a twisted analog of our recent work on vertex representations and the McKay correspondence. For each finite group $Γ$ and a virtual character of $Γ$ we construct twisted vertex operators on the Fock space spanned by the super spin characters of the spin wreath products $Γ\wr\widetilde{S}_n$ of $Γ$ and a double cover of the symmetric group $S_n$ for all $n$. When $Γ$ 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 $Γ$ is an arbitrary finite group and the virtual character is trivial, our vertex operator construction yields the spin character tables for $Γ\wr\widetilde{S}_n$. |
| title | Twisted vertex representations via spin groups and the McKay correspondence |
| topic | Quantum Algebra Representation Theory 17B, 20C |
| url | https://arxiv.org/abs/math/0007159 |