Moment graphs and Kazhdan-Lusztig polynomials
نویسنده
چکیده
Motivated by a result of Fiebig (2007), we categorify some properties of Kazhdan-Lusztig polynomials via sheaves on Bruhat moment graphs. In order to do this, we develop new techniques and apply them to the combinatorial data encoded in these moment graphs. Résumé. Motivés par un resultat de Fiebig (2007), nous categorifions certaines propriétés des polynômes de KazhdanLusztig en utilisant faisceaux sur les graphes moment de Bruhat. Pour faire ça, nous développons de nouvelles techniques et les appliquons ensuite aux données combinatoires encodées dans ces graphes moment.
منابع مشابه
Combinatorics on Bruhat Graphs and Kazhdan-Lusztig Polynomials
the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Abstract We establish three new combinatorial results on a relation between irregularity of Bruhat graphs and Kazhdan-Lusztig polynomials for Bruhat intervals in all crystallographic Coxeter systems. For our discussion, De-odhar's ...
متن کاملSpecial matchings and Kazhdan-Lusztig polynomials
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 pol...
متن کاملLinear Algebra Construction of Formal Kazhdan-lusztig Bases
General facts of linear algebra are used to give proofs for the (wellknown) existence of analogs of Kazhdan-Lusztig polynomials corresponding to formal analogs of the Kazhdan-Lusztig involution, and of explicit formulae (some new, some known) for their coefficients in terms of coefficients of other natural families of polynomials (such as the corresponding formal analogs of the Kazhdan-Lusztig ...
متن کاملParabolic Kazhdan-lusztig Polynomials for Hermitian Symmetric Pairs
We study the parabolic Kazhdan-Lusztig polynomials for Hermitian symmetric pairs. In particular, we show that these polynomials are always either zero or a monic power of q, and that they are combinatorial invariants.
متن کاملM ay 2 00 8 Leading coefficients of the Kazhdan - Lusztig polynomials for an Affine Weyl group of type
In this paper we compute the leading coefficients μ(y,w) of the Kazhdan-Lusztig polynomials Py,w for an affineWeyl group of type B̃2. When a(y) ≤ a(w) or a(y) = 2 and a(w) = 1, we compute all μ(y,w) clearly, where a(y) is the a-function of a Coxeter group defined by Lusztig (see [L1]). With these values μ(y,w), we are able to show that a conjecture of Lusztig on distinguished involutions is true...
متن کامل