Polynomiality of Grothendieck groups for finite general linear groups, Deligne-Lusztig characters, and injective unstable modules
@article{Perennou2019PolynomialityOG, title={Polynomiality of Grothendieck groups for finite general linear groups, Deligne-Lusztig characters, and injective unstable modules}, author={H'elene P'erennou}, journal={arXiv: Representation Theory}, year={2019} }
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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