Tomoyuki Arakawa

Associated Varieties of Modules Over Kac–Moody Algebras and C2-Cofiniteness of W-Algebras

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.

Rationality of W-algebras: principal nilpotent cases

We prove the rationality of all the minimal series principal W -algebras discovered by Frenkel, Kac and Wakimoto, thereby giving a new family of rational and C2-conite vertex operator algebras. A key ingredient in our proof is the study of Zhu’s algebra of simple W -algebras via the quantized Drinfeld-Sokolov reduction. We show that the functor of taking Zhu’s algebra commutes with the reduction functor. Using this general fact we determine the maximal spectrums of the associated graded of Zhu’s algebras of vertex operator algebras associated with admissible representations of ane Kac-Moody algebras as well.

Spectral Decomposition of Path Space in Solvable Lattice Model

AbstractWe give thespectral decomposition of the path space of the

JOSEPH IDEALS AND LISSE MINIMAL -ALGEBRAS

U_q (\widehat{sl}_2 )

The linkage principle for restricted critical level representations of affine Kac–Moody algebras

vertex model with respect to the local energy functions. The result suggests the hidden Yangian module structure on the

Two-sided BGG resolutions of admissible representations

\widehat{sl}_2