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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Special matchings and parabolic Kazhdan-Lusztig polynomials

Author: Mario Marietti
Journal: Trans. Amer. Math. Soc. 368 (2016), 5247-5269
MSC (2010): Primary 05E99, 20F55
Published electronically: June 18, 2015
MathSciNet review: 3456179
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Abstract: We prove that the combinatorial concept of a special matching can be used to compute the parabolic Kazhdan-Lusztig polynomials of doubly laced Coxeter groups and of dihedral Coxeter groups. In particular, for this class of groups which includes all Weyl groups, our results generalize to the parabolic setting the main results in Advances in Math. 202 (2006), 555-601. As a consequence, the parabolic Kazhdan-Lusztig polynomial indexed by $ u$ and $ v$ depends only on the poset structure of the Bruhat interval from the identity element to $ v$ and on which elements of that interval are minimal coset representatives.

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Mario Marietti
Affiliation: Dipartimento di Ingegneria Industriale e Scienze Matematiche, Università Politecnica delle Marche, Via Brecce Bianche, 60131 Ancona, Italy

Keywords: Kazhdan--Lusztig polynomials, Coxeter groups, special matchings
Received by editor(s): May 8, 2014
Received by editor(s) in revised form: July 20, 2014, September 14, 2014, and November 23, 2014
Published electronically: June 18, 2015
Article copyright: © Copyright 2015 American Mathematical Society

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