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 are proven to be of importance in several areas in 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 result imply, and generalize, the recent one in [F. du Cloux, Rigidity of Schubert closures and invariance of Kazhdan-Lusztig polynomials, Advances in Math. 180 (2003), 146-175] on the combinatorial invariance of Kazhdan-Lusztig polynomials.
Special matchings and Kazhdan-Lusztig polynomials
CASELLI, FABRIZIO;
2006
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 are proven to be of importance in several areas in 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 result imply, and generalize, the recent one in [F. du Cloux, Rigidity of Schubert closures and invariance of Kazhdan-Lusztig polynomials, Advances in Math. 180 (2003), 146-175] on the combinatorial invariance of Kazhdan-Lusztig polynomials.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
