Rationality of admissible affine vertex algebras in the category O
Rationality of admissible affine vertex algebras in the category O
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DOI：
10.1215/00127094-3165113
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发表时间：
2012-07
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影响因子：
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通讯作者：
T. Arakawa
中科院分区：
文献类型：
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作者：
T. Arakawa
研究了仿射Kac-Moody代数在分数阶上的模不变表示的顶点代数，该代数的简单最高权模由Joseph的特征变体分类。证明了在可容许水平k上的非扭曲仿射Kac-Moody代数的不可约最高权表示是相关简单仿射顶点代数上的模，当且仅当它是一个积分根与顶点代数本身同构的可容许表示。这特别证明了Adamovic和Milas关于O范畴中可容许仿射顶点代数的合理性的猜想。
We study the vertex algebras associated with modular invariant representations of affine Kac-Moody algebras at fractional levels, whose simple highest weight modules are classified by Joseph's characteristic varieties. We show that an irreducible highest weight representation of a non-twisted affine Kac-Moody algebra at an admissible level k is a module over the associated simple affine vertex algebra if and only if it is an admissible representation whose integral root system is isomorphic to that of the vertex algebra itself. This in particular proves the conjecture of Adamovic and Milas on the rationality of admissible affine vertex algebras in the category O.