Certain complex representations of SL₂(\mathbbF_q)

2022/06/01 by Junbin Dong, Dong, Junbin
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Finite Group Theory Research #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2206.00183

openalex publication_date 2022/06/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We introduce the representation category \mathscrC(\bf G) for a connected reductive algebraic group \bf G which is defined over a finite field \mathbbF_q of q elements. We show that this category has many good properties for \bf G=SL₂(\mathbbF_q). In particular, it is an abelian category and a highest weight category. Moreover, we classify the simple objects in \mathscrC(\bf G) for \bf G=SL₂(\mathbbF_q).

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