4,001 research outputs found
Associated varieties of modules over Kac-Moody algebras and -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.Comment: revised, to appear in IMR
A vertex algebra attached to the flag manifold and Lie algebra cohomology
Each flag manifold carries a unique algebra of chiral differential operators.
Continuing along the lines of arXiv:0903.1281 we compute the vertex algebra
structure on the cohomology of this algebra. The answer is: the tensor product
of the center and a subalgebra; the center is isomorphic, as a commutative
associative algebra, to the cohomology of the corresponding maximal nilpotent
Lie algebra; the subalgebra is the vacuum module over the corresponding affine
Lie algebra of critical level and 0 central character. We next find the
Friedan-Martinec-Shenker-Borisov bosonization of the cohomology algebra in case
of the projective line and show that this algebra vanishes nonperturbatively,
thus verifying a suggestion by Witten.Comment: a reference adde
Localization of affine W-algebras
We introduce the notion of an asymptotic algebra of chiral differential
operators. We then construct, via a chiral Hamiltonian reduction, one such
algebra over a resolution of the intersection of the Slodowy slice with the
nilpotent cone. We compute the space of global sections of this algebra thereby
proving a localization theorem for affine W-algebras at the critical level.Comment: 36 page
A chiral Borel-Weil-Bott theorem
We compute the cohomology of modules over the algebra of twisted chiral
differential operators over the flag manifold. This is applied to (1) finding
the character of -integrable irreducible highest weight modules over the
affine Lie algebra at the critical level, and (2) computing a certain elliptic
genus of the flag manifold. The main tool is a result that interprets the
Drinfeld-Sokolov reduction as a derived functor.Comment: Some considerable reworking. A final version to appear in Adv. in
Mat
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