相关论文: Fully commutative Kazhdan-Lusztig cells
An element of a Coxeter group $W$ is fully commutative if any two of its reduced decompositions are related by a series of transpositions of adjacent commuting generators. These elements were extensively studied by Stembridge, in particular…
In a Coxeter group $W$, an element is fully commutative if any two of its reduced expressions can be linked by a series of commutation of adjacent letters. These elements have particularly nice combinatorial properties, and also index a…
In this thesis, I present an associative diagram algebra that is a faithful representation of a particular Temperley--Lieb algebra of type affine $C$, which has a basis indexed by the fully commutative elements of the Coxeter group of the…
We extend the usual notion of fully commutative elements from the Coxeter groups to the complex reflection groups. Then we decompose the sets of fully commutative elements into natural subsets according to their combinatorial properties,…
The purpose of this article is to shed new light on the combinatorial structure of Kazhdan-Lusztig cells in infinite Coxeter groups $W$. Our main focus is the set $\D$ of distinguished involutions in $W$, which was introduced by Lusztig in…
In this paper, we decompose the set of fully commutative elements into natural subsets when the Coxeter group is of type $D_n$, and study the combinatorics of these subsets, revealing hidden structures. (We do not consider type $A_n$ first,…
Following Lusztig, we consider a Coxeter group $W$ together with a weight function. Geck showed that the Kazhdan-Lusztig cells of $W$ are compatible with parabolic subgroups. In this paper, we generalize this argument to some subsets of $W$…
We study the combinatorics of fully commutative elements in Coxeter groups of type $H_n$ for any $n > 2$. Using the results, we construct certain canonical bases (i.e., IC bases) for non-simply-laced generalized Temperley--Lieb algebras and…
We compare the canonical basis for a generalized Temperley-Lieb algebra of type A or B with the Kazhdan-Lusztig basis for the corresponding Hecke algebra.
In this paper, we present an infinite dimensional associative diagram algebra that satisfies the relations of the generalized Temperley--Lieb algebra having a basis indexed by the fully commutative elements (in the sense of Stembridge) of…
In this paper, we let $\Hecke$ be the Hecke algebra associated with a finite Coxeter group $W$ and with one-parameter, over the ring of scalars $\Alg=\mathbb{Z}(q, q^{-1})$. With an elementary method, we introduce a cellular basis of…
We study two families of polynomials that play the same role, in the generalized Temperley Lieb algebra of a Coxeter group, as the Kazhdan Lusztig and R polynomials in the Hecke algebra of the group. Our results include recursions, closed…
In this paper, we study the Kazhdan--Lusztig cells of a Coxeter group $W$ in a ``relative'' setting, with respect to a parabolic subgroup $W_I \subseteq W$. This relies on a factorization of the Kazhdan--Lusztig basis $\{C_w\}$ of the…
We define ``star reducible'' Coxeter groups to be those Coxeter groups for which every fully commutative element (in the sense of Stembridge) is equivalent to a product of commuting generators by a sequence of length-decreasing star…
In this article, we study the \'etale cohomology of the compactification of Deligne-Lusztig varieties associated to a Coxeter element. We prove a result for the integral coefficients in the case of general linear group $GL_d$, and we…
We classify a class of complex representations of an arbitrary Coxeter group via characters of the integral homology of certain graphs. Such representations can be viewed as a generalization of the geometric representation and correspond to…
We establish the existence of an IC basis for the generalized Temperley--Lieb algebra associated to a Coxeter system of arbitrary type. We determine this basis explicitly in the case where the Coxeter system is simply laced and the algebra…
We classify fully commutative elements in the affine Coxeter group of type $\tilde{A_{n}}$. We give a normal form for such elements, then we propose an application of this normal form: we lift these fully commutative elements to the affine…
We consider the set $\Irr(W)$ of (complex) irreducible characters of a finite Coxeter group $W$. The Kazhdan--Lusztig theory of cells gives rise to a partition of $\Irr(W)$ into "families" and to a natural partial order $\leq_{\cLR}$ on…
We explain a strategy for a proof of the positivity of all coefficients of Kazhdan-Lusztig-polynomials for arbitrary Coxeter groups by constructing spaces whose dimensions we conjecture to be these coefficients.