On endomorphism algebras arising from Hecke algebras
The endomorphism algebras associated to Hecke algebras of type \(D\) with odd ranks are studied. A number of authors have studied the cases when the endomorphism algebras are associated to the Hecke algebras of types \(A_{n-1}\), \(B_n\) and \(C_n\) or more generally, \(G(r,1,n)\). It turns out that the cellular basis (or more generally, standard basis) of Hecke algebras is important in the study of these endomorphism algebras. The notion of standardly based algebras was introduced by \textit{J. Du} and \textit{H. Rui} [in Trans. Am. Math. Soc. 350, No. 8, 3207-3235 (1998; Zbl 0908.16015)] and these are generalized versions of cellular algebras introduced by \textit{J. J. Graham} and \textit{G. I. Lehrer} [in Invent. Math. 123, No. 1, 1-34 (1996; Zbl 0853.20029)]. Two standard bases for Hecke algebras \(\mathcal H\) of type \(D\) with odd ranks are constructed in this paper under the assumption that a certain polynomial in \(q\) is nonzero. It is then shown that the endomorphism algebras associated to Hecke algebras \(\mathcal H\) are standardly based algebras and indeed quasi-hereditary.
scientific article; zbMATH DE number 1275268