1004.1554 (Tomoyuki Arakawa)

Associated varieties of modules over Kac-Moody algebras and
$C_2$-cofiniteness of W-algebras    [PDF]

Tomoyuki Arakawa

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 $\Ad G$-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.

View original: http://arxiv.org/abs/1004.1554