142 research outputs found
Drinfeld Functor and Finite-Dimensional Representations of Yangian
We extend the results of Drinfeld on Drinfeld functor to the case l>n. We
present the character of finite-dimensional representations of the Yangian
Y(sl_n) in terms of the Kazhdan-Lusztig polynomials as a consequence.Comment: Latex2e, 17pages, corrected typo
Rationality of admissible affine vertex algebras in the category O
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.Comment: Improved exposition, to appear in Duke Math.
Two-sided BGG resolutions of admissible representations
We prove the conjecture of Frenkel, Kac and Wakimoto on the existence of
two-sided BGG resolutions of G-integrable admissible representations of affine
Kac-Moody algebras at fractional levels. As an application we establish the
semi-infintie analogue of the generalized Borel-Weil theorem for mimimal
parabolic subalgebras which enables an inductive study of admissible
representations.Comment: revised, to appear in Representation Theor
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 in 1992, thereby giving a new family of
rational and C_2-cofinite 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 algebra of all the
admissible affine vertex algebras as well.Comment: revised, to appear in Annals of Mat
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