A Localization Theorem for Finite W-algebras
Christopher Dodd, Kobi Kremnizer
TL;DR
This paper provides a geometric interpretation of module categories over finite W-algebras, offering new insights and reestablishing key equivalences in the representation theory of these algebras.
Contribution
It introduces a localization theorem for finite W-algebras, extending geometric methods to their module categories and rederiving the Skryabin equivalence.
Findings
Geometric interpretation of finite W-algebra modules
Reproof of the Skryabin equivalence using geometric methods
Extension of Beilinson-Bernstein and Kashiwara-Rouquier frameworks
Abstract
Following the work of Beilinson-Bernstein and Kashiwara-Rouquier, we give a geometric interpretation of certain categories of modules over the finite W-algebra. As an application we reprove the Skryabin equivalence.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Homotopy and Cohomology in Algebraic Topology · Advanced Topics in Algebra