Special matchings and Kazhdan-Lusztig polynomials |
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Authors: | Francesco Brenti Fabrizio Caselli |
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Affiliation: | a Dipartimento di Matematica, Università di Roma “Tor Vergata”, Via della Ricerca Scientifica, 1 00133 Roma, Italy b Institut Girard Desargues, Université Claude Bernard Lyon 1 21 Avenue Claude Bernard, 69622 Villeurbanne, France |
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Abstract: | In 1979 Kazhdan and Lusztig defined, for every Coxeter group W, a family of polynomials, indexed by pairs of elements of W, which have become known as the Kazhdan-Lusztig polynomials of W, and which have proven to be of importance in several areas of mathematics. In this paper, we show that the combinatorial concept of a special matching plays a fundamental role in the computation of these polynomials. Our results also imply, and generalize, the recent one in [Adv. in Math. 180 (2003) 146-175] on the combinatorial invariance of Kazhdan-Lusztig polynomials. |
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Keywords: | 05E99 20F55 |
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