Vanishing of cohomology associated to quantized Drinfeld-Sokolov reduction

Abstract

We prove a vanishing theorem of the cohomology arising from the two Quantized Drinfeld-Sokolov reductions (``+'' and ``-'' reduction) introduced by Feigin-Frenkel and Frenkel-Kac-Wakimoto. As a consequence, the vanishing conjecture of Frenkel-Kac-Wakimoto is proved for the ``-'' reduction and partially for the ``+'' reduction.

to appear in Int. Math. Res. Not.; 28 pages ; v2 adds a new section, v3: minor revisions and typos (including the author's name)

References in corpus (3)

• Vertex Algebras and Algebraic Curves
• Characters of irreducible modules with non-critical highest weights over affine Lie algebras
• Kazhdan-Lusztig tensoring and Harish-Chandra categories

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• Representation Theory of Superconformal Algebras and the Kac-Roan-Wakimoto Conjecture
• Ordinary modules for vertex algebras of ${\mathfrak{osp}}_{1|2n}$
• A chiral Borel-Weil-Bott theorem
• On functors associated to a simple root
• Quantized Reductions and Irreducible Representations of W-Algebras
• The Drinfeld--Sokolov reduction of admissible representations of affine Lie algebras