Kazhdan-Lusztig tensoring and Harish-Chandra categories
I.B.Frenkel, F.Malikov
TL;DR
This paper explores the use of Kazhdan-Lusztig tensoring to define affine translation functors, analyze annihilating ideals of affine Lie algebra modules, and propose a functorial approach to affine Harish-Chandra bimodules.
Contribution
It introduces a novel application of Kazhdan-Lusztig tensoring to affine translation functors and connects annihilating ideals with vertex operator algebras, advancing the understanding of affine Harish-Chandra categories.
Findings
Defined affine translation functors using Kazhdan-Lusztig tensoring
Characterized annihilating ideals via vertex operator algebras
Outlined a functorial framework for affine Harish-Chandra bimodules
Abstract
We use the Kazhdan-Lusztig tensoring to define affine translation functors, describe annihilating ideals of highest weight modules over an affine Lie algebra in terms of the corresponding VOA, and to sketch a functorial approach to ``affine Harish-Chandra bimodules''.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Advanced Algebra and Geometry