Associated Varieties of Modules Over Kac–Moody Algebras and C2-Cofiniteness of W-Algebras
Associated Varieties of Modules Over Kac–Moody Algebras and C2-Cofiniteness of W-Algebras
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DOI：
10.1093/imrn/rnu277
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发表时间：
2010-04
影响因子：
1
通讯作者：
T. Arakawa
中科院分区：
文献类型：
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作者：
T. Arakawa
首先，我们建立了Kac-Moody代数上的模簇与仿射W-代数上的模簇之间的关系。其次，我们证明了G-可积可容许表示的奇异支集上的Feigin-Frenkel猜想。事实上，我们通过显式确定G-可积可容许表示的相关变量，证明了它们是G的零锥的不可约G-不变子簇。第三，我们证明了大量简单W-代数的C_2-余有限性，包括所有极小级数主W-代数和Kac-Wakimoto最近发现的例外W-代数。
First, we establish the relation between the associated varieties of modules over Kac-Moody algebras \hat{g} and those over affine W-algebras. Second, we prove the Feigin-Frenkel conjecture on the singular supports of G-integrable admissible representations. In fact we show that the associated variates of G-integrable admissible representations are irreducible G-invariant subvarieties of the nullcone of g, by determining them explicitly. Third, we prove the C_2-cofiniteness of a large number of simple W-algebras, including all minimal series principal W-algebras and the exceptional W-algebras recently discovered by Kac-Wakimoto.