An explicit bound is given for functions of conditionally negative type on Kazhdan groups, in terms of a set of generators and the corresponding Kazhdan constants. This is used to estimate how far a set in an infinite measure space can be translated by the action of a Kazhdan group. Some estimates are given for Kazhdan constants.

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 ...

We give bounds on Kazhdan constants of abelian extensions of (finite) groups. As a corollary, we improved known results of Kazhdan constants for some meta-abelian groups and for the relatively free group in the variety of p-groups of lower p-series of class 2. Furthermore, we calculate Kazhdan constants of the tame automorphism groups of the free nilpotent groups.

Let (W,S) be a Coxeter system. A W -graph is an encoding of a representation of the corresponding Iwahori-Hecke algebra. Especially important examples include the W -graph corresponding to the action of the Iwahori-Hecke algebra on the Kazhdan-Lusztig basis as well as this graph’s strongly connected components (cells). In 2008, Stembridge identified some common features of the Kazhdan-Lusztig g...

We investigate the compatibility of the set of fully commutative elements of a Coxeter group with the various types of Kazhdan–Lusztig cells using a canonical basis for a generalized version of the Temperley–Lieb algebra. Cellules pleinement commutatives de Kazhdan–Lusztig Nousétudions la compatibilité entre l'ensemble deséléments pleinement commu-tatifs d'un groupe de Coxeter et les divers typ...

We introduce the Z-polynomial of a matroid, which we define in terms of the Kazhdan-Lusztig polynomial. We then exploit a symmetry of the Z-polynomial to derive a new recursion for Kazhdan-Lusztig coefficients. We solve this recursion, obtaining a closed formula for Kazhdan-Lusztig coefficients as alternating sums of multi-indexed Whitney numbers. For realizable matroids, we give a cohomologica...

These are notes for a talk on Kazhdan-Lusztig Cells for Hecke Algebras. In this talk, we construct the Kazhdan-Lusztig basis for the Hecke algebra associated to an arbitrary Coxeter group, in full multiparameter generality. We then use this basis to construct a partition of the Coxeter group into the Kazhdan-Lusztig cells and describe the corresponding cell representations. Finally, we speciali...

We study the relationships between three different classes of sequences (or sets) integers, namely rigidity sequences, Kazhdan and nullpotent sequences. prove that are non-Kazhdan nullpotent, all other implications false. In particular, we show by probabilistic means there exist integers which both Kazhdan. Moreover, using Baire category methods, provide general criteria for a sequence to be se...

We study two bases of the vector space of immanants of C[x1,1, . . . , xn,n]: the bitableaux basis of Désarménien-Kung-Rota, and a subset of the dual canonical basis called the basis of Kazhdan-Lusztig immanants. We show that the transition matrix between these bases is unitriangular, describe new vanishing results for the Kazhdan-Lusztig immanants, and relate both bases to other immanants defi...

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...