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

Hélène Pérennou (1)

1 LMJL - Laboratoire de Mathématiques Jean Leray

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.

Domaines: Théorie des représentations [math.RT]; Topologie algébrique [math.AT]

Hélène Pérennou. Polynomiality of Grothendieck groups for finite general linear groups, Deligne-Lusztig characters, and injective unstable modules. 2019. ⟨hal-02006864⟩