The block decomposition of the principal representation category of reductive algebraic groups with Frobenius maps

2025/06/25 by Xiaoyu Chen, Chen, Xiaoyu, Junbin Dong +1
Mathematics · #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #FOS: Mathematics #Finite Group Theory Research #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2506.20378

openalex publication_date 2025/06/25 · openalex created_date 2025/10/09 · openalex updated_date 2026/07/28

Abstract

Let \bf G be a connected reductive algebraic group defined over the finite field \mathbbF_q with q elements. Let \Bbbk be a field such that \opchar \Bbbk ≠ \opchar \mathbbF_q. In this paper, we study the extensions of simple modules (over \Bbbk) in the principal representation category \mathscrO(\bf G) which is defined in \citeD1. In particular, we get the block decomposition of \mathscrO(\bf G), which is parameterized by the central characters of \bf G.

Citations

• On the extensions of certain representations of reductive algebraic groups with Frobenius maps
• Abstract induced modules for reductive algebraic groups with Frobenius maps

Related

• On the extensions of certain representations of reductive algebraic groups with Frobenius maps
• The Principal Representations of Reductive Algebraic Groups with Frobenius Maps
• Towards a Jordan decomposition of blocks of finite reductive groups
• Abstract induced modules for reductive algebraic groups with Frobenius maps
• Complex representations of reductive algebraic groups with Frobenius maps in the category \mathscrX