Stratifying endomorphism algebras associated to Hecke algebras
Let \(G\) be a finite group of Lie type and let \(k\) be a field of characteristic distinct from the defining characteristic of \(G\). This paper presents a systematic study of the structure and homological algebra for the endomorphism algebra \(S(G,k)=\text{End}_{kG}\bigl(\bigoplus_J\text{Ind}^G_{P_J}k\bigr)\). The structure of this algebra turns out to involve new applications of Kazhdan-Lusztig cell theory. Two stratification conjectures made by \textit{E. Chine}, \textit{B. Parshall} and \textit{L. Scott} [Mem. Am. Math. Soc. 591 (1996; Zbl 0888.16006)] are proved. Also the authors formulate a new conjecture about the structure of \(S(G,k)\).
scientific article; zbMATH DE number 1203911
scientific article