Alvis-curtis duality on lowercase q-schur and hecke algebras

• Autores: Sibylle Schroll
• Localización: Quarterly journal of mathematics, ISSN 0033-5606, Vol. 58, Nº. 2, 2007, págs. 255-263
• Idioma: inglés
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• Resumen

  • We show that for a finite reductive group tensoring with a quotient of the complex inducing the Alvis¿Curtis character duality induces a self-derived equivalence on a quotient of the group algebra. In the case of general linear groups, this equivalence realizes an equivalence between derived categories of q-Schur algebras. Furthermore, in the latter case, multiplication of the quotient complex by an idempotent induces an isomorphism with the two-sided q-analogue of the Coxeter complex.