Rationality and fusion rules of exceptional $mathcal {W}$-algebras
抄録
First, we prove the Kac–Wakimoto conjecture on modular invariance of characters of exceptional affine $mathcal {W}$-algebras. In fact more generally we prove modular invariance of characters of all lisse $mathcal {W}$-algebras obtained through Hamiltonian reduction of admissible affine vertex algebras. Second, we prove the rationality of a large subclass of these $mathcal {W}$-algebras, which includes all exceptional $mathcal {W}$-algebras of type $mathcal {A}$ and lisse subregular $mathcal {W}$-algebras in simply laced types. Third, for the latter cases we compute $mathcal {S}$-matrices and fusion rules. Our results provide the first examples of rational $mathcal {W}$-algebras associated with nonprincipal distinguished nilpotent elements, and the corresponding fusion rules are rather mysterious
収録刊行物
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- Journal of the European Mathematical Society
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Journal of the European Mathematical Society 25 (7), 2763-2813, 2023-07-07
European Mathematical Society - EMS - Publishing House GmbH
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キーワード
詳細情報 詳細情報について
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- CRID
- 1050297659216126464
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- ISSN
- 14359863
- 14359855
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- HANDLE
- 2433/285245
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- 本文言語コード
- en
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- 資料種別
- journal article
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- データソース種別
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- IRDB