Stratifying endomorphism algebras using exact categories
This paper is the second in a series aimed at proving versions of a conjecture made by the authors in 1996. The conjecture concerns the enlargement, in a framework involving Kazhdan-Lusztig cell theory, of those Hecke endomorphism algebras which occur naturally in the cross characteristic representation theory of finite groups of Lie type. See [the authors, J. Algebra 203, No. 1, 169--210 (1998; Zbl 0920.20008)] for the original version of the conjecture, and [the authors, Pac. J. Math. 279, No. 1--2, 229--254 (2015; Zbl 1365.20004)] for a reformulation. This paper under review constructs enlargements of Hecke algebras over \(\mathbb{Z}[t, t^{-1} ]\) to certain standardly stratified algebras. The latter are obtained as endomorphism algebras of modules with dual left cell module filtrations in the sense of Kazhdan-Lusztig. A novel feature of the proofs is the use of suitably chosen exact categories to avoid difficult \(\text{Ext}^1\)-vanishing conditions.
scientific article; zbMATH DE number 6690399
scientific article