Character sheaves on loop Lie algebras: polar partition

2025/06/17 by Ngô Bảo Châu, Chau, Ngo Bao, Zhiwei Yun +1 · 1 citation
Mathematics · #14F08 #22E50 #22E67 #Advanced Topics in Algebra #FOS: Mathematics #Finite Group Theory Research #Mathematics and Applications #Number Theory (math.NT) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2506.14584

openalex publication_date 2025/06/17 · openalex created_date 2025/10/13 · openalex updated_date 2026/07/28

Abstract

In this paper we propose a partition of loop Lie algebras into invariant sets parametrized by polar data. Our polar partition is motivated by J-K. Yu's construction of supercuspidal representations and leads to a conjectural construction of character sheaves on loop Lie algebras.

Citations

• Counting absolutely indecomposable G-bundles
• Generic character sheaves on parahoric subgroups
• Geometric representations of graded and rational Cherednik algebras
• Codimensions of root valuation strata
• Character Sheaves on Reductive Lie Algebras

Cited by

• An alternative construction of character sheaves on parahoric subgroups

Related

• Invariant systems and character sheaves for graded Lie algebras
• Cuspidal character sheaves on graded Lie algebras II
• Cuspidal character sheaves on graded Lie algebras
• Character Sheaves on Reductive Lie Algebras
• Modular Character Sheaves on Reductive Lie Algebras