### 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 language | English |
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Pages (from-to) | 128-134 |

Number of pages | 6 |

Journal | Journal of Algebra |

Volume | 289 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2005 |

### Cite this

*Journal of Algebra*,

*289*(1), 128-134. https://doi.org/10.1016/j.jalgebra.2005.03.026

**A two-sided q-analogue of the Coxeter complex.** / Linckelmann, Markus; Schroll, S.

Research output: Contribution to journal › Article

*Journal of Algebra*, vol. 289, no. 1, pp. 128-134. https://doi.org/10.1016/j.jalgebra.2005.03.026

}

TY - JOUR

T1 - A two-sided q-analogue of the Coxeter complex

AU - Linckelmann, Markus

AU - Schroll, S.

PY - 2005

Y1 - 2005

N2 - 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.

AB - 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.

U2 - 10.1016/j.jalgebra.2005.03.026

DO - 10.1016/j.jalgebra.2005.03.026

M3 - Article

VL - 289

SP - 128

EP - 134

JO - Journal of Algebra

JF - Journal of Algebra

SN - 0021-8693

IS - 1

ER -