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. (c) 2005 Elsevier Inc. All rights reserved.
Brenti, F., Caselli, F., Marietti, M. (2006). Special matchings and Kazhdan-Lusztig polynomials. ADVANCES IN MATHEMATICS, 202(2), 555-601 [10.1016/j.aim.2005.01.011].
Special matchings and Kazhdan-Lusztig polynomials
BRENTI, FRANCESCO;
2006-01-01
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. (c) 2005 Elsevier Inc. All rights reserved.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.