Special matchings and Kazhdan-Lusztig polynomials
نویسندگان
چکیده
In 1979 Kazhdan and Lusztig defined, for every Coxeter group W , a family of polynomials, indexed by pairs of elements ofW , 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 [12] on the combinatorial invariance of Kazhdan-Lusztig polynomials.
منابع مشابه
Combinatorial invariance of Kazhdan-Lusztig polynomials on intervals starting from the identity
We show that for Bruhat intervals starting from the identity in Coxeter groups the conjecture of Lusztig and Dyer holds, that is, the R-polynomials and the Kazhdan-Lusztig polynomials defined on [e, u] only depend on the isomorphism type of [e, u]. To achieve this we use the purely poset-theoretic notion of special matching. Our approach is essentially a synthesis of the explicit formula for sp...
متن کاملThe Kazhdan-Lusztig polynomial of a matroid
We associate to every matroid M a polynomial with integer coefficients, which we call the Kazhdan-Lusztig polynomial of M , in analogy with Kazhdan-Lusztig polynomials in representation theory. We conjecture that the coefficients are always non-negative, and we prove this conjecture for representable matroids by interpreting our polynomials as intersection cohomology Poincaré polynomials. We al...
متن کاملBrundan-kazhdan-lusztig and Super Duality Conjectures
We formulate a general super duality conjecture on connections between parabolic categories O of modules over Lie superalgebras and Lie algebras of type A, based on a Fock space formalism of their Kazhdan-Lusztig theories which was initiated by Brundan. We show that the Brundan-Kazhdan-Lusztig (BKL) polynomials for gl(m|n) in our parabolic setup can be identified with the usual parabolic Kazhda...
متن کاملComposition Kostka functions
Macdonald defined two-parameter Kostka functions Kλμ(q, t) where λ, μ are partitions. The main purpose of this paper is to extend his definition to include all compositions as indices. Following Macdonald, we conjecture that also these more general Kostka functions are polynomials in q and t with non-negative integers as coefficients. If q = 0 then our Kostka functions are Kazhdan-Lusztig polyn...
متن کاملTwisted Incidence Algebras and Kazhdan-Lusztig-Stanley functions
We introduce a new multiplication in the incidence algebra of a partially ordered set, and study the resulting algebra. As an application of the properties of this algebra we obtain a combinatorial formula for the Kazhdan-Lusztig-Stanley functions of a poset. As special cases this yields new combinatorial formulas for the parabolic and inverse parabolic Kazhdan-Lusztig polyno-mials, for the gen...
متن کامل