Koszul duality for Kac-Moody groups and characters of tilting modules

2017/06/01 by Pramod N. Achar, Shotaro Makisumi, Achar, Pramod +5 · 3 citations
Mathematics · #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1706.00183

openalex publication_date 2017/06/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We establish a character formula for indecomposable tilting modules for connected reductive groups in characteristic p in terms of p-Kazhdan-Lusztig polynomials, for p>h the Coxeter number. Using results of Andersen, one may deduce a character formula for simple modules if p>2h-3. Our results are a consequence of an extension to modular coefficients of a monoidal Koszul duality equivalence established by Bezrukavnikov and Yun.

Cited by

• Non-homogeneous Koszul duality in representation theory
• Tilting modules for reductive algebraic groups: characters and support varieties
• Intersection cohomology without spaces

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