Polynomiality of Grothendieck groups for finite general linear groups, Deligne-Lusztig characters, and injective unstable modules

2019/02/05 by Hélène Pérennou, Pérennou, Hélène
Mathematics · #Advanced Algebra and Geometry #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Finite Group Theory Research #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1902.01610

openalex publication_date 2019/02/05 · openalex created_date 2019/03/02 · openalex updated_date 2026/07/28

Abstract

Let K 0 (Fp GLn(Fp)-proj) denote the Grothendieck group of finitely generated pro-jective Fp GLn(Fp)-modules. We show that the algebra C ⊗ n≥0 K 0 (Fp GLn(Fp)-proj) with multiplication given by induction functors, is a polynomial algebra. We explicit generators and their relation with Deligne-Lusztig characters.

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