The Kazhdan-Lusztig conjecture for W-algebras

Abstract

The main result in this paper is the character formula for arbitrary irreducible highest weight modules of W algebras. The key ingredient is the functor provided by quantum Hamiltonian reduction, that constructs the W algebras from affine Kac-Moody algebras and in a similar fashion W modules from KM modules. Assuming certain properties of this functor, the W characters are subsequently derived from the Kazhdan-Lusztig conjecture for KM algebras. The result can be formulated in terms of a double coset of the Weyl group of the KM algebra: the Hasse diagrams give the embedding diagrams of the Verma modules and the Kazhdan-Lusztig polynomials give the multiplicities in the characters.

uuencoded file, 29 pages latex, 5 figures

References in corpus (8)

• W-symmetry in Conformal Field Theory
• The Relation between Quantum W algebras and Lie algebras
• On the Landau-Ginzburg Realization of Topological Gravities
• Semi-infinite cohomology of W-algebras
• The Kazhdan-Lusztig conjecture for finite W-algebras
• $c=r_g$ Theories of $W_G$-Gravity: The Set of Observables as a Model of Simply Laced $G$
• On the Algebraic Structure of Gravitational Descendants in CP(n-1) Coset Models
• On the BRST structure of W_3 gravity coupled to c=2 matter

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• Highest weight representations of the N=1 Ramond algebra
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• On parafermion vertex algebras of $\mathfrak{sl}(2{)}_{-3/2}$ and $\mathfrak{sl}(3{)}_{-3/2}$
• The W_3 algebra: modules, semi-infinite cohomology and BV-algebras
• Affine characters at negative level and elliptic genera of non-critical strings
• Gauging Wess-Zumino-Witten Models