A two-sided q-analogue of the Coxeter complex

Markus Linckelmann, S. Schroll

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

We define a complex of bimodules over the Iwahori-Hecke algebra associated to a finite Coxeter group, calculate its cohomology and show that it induces a derived equivalence over its module category extending the Morita equivalence given by a certain algebra automorphism. We show further that when tensored with the index representation this complex becomes isomorphic to the one-sided q-analogue of the Coxeter complex previously defined by V. Deodhar [On some geometric aspects of Bruhat orderings. II. The parabolic analogue of Kazhdan-Lusztig polynomials, J. Algebra 111 (2) (1987) 483-506] and A. Mathas [A q-analogue of the Coxeter complex, J. Algebra 164 (3) (1994) 831-848]. (c) 2005 Elsevier Inc. All rights reserved.

Original languageEnglish
Pages (from-to)128-134
Number of pages6
JournalJournal of Algebra
Volume289
Issue number1
DOIs
Publication statusPublished - 2005

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