Related papers: Kazhdan-Lusztig left cells in type $B_n$ for inter…

We describe the equivariant K-groups of a family of generalized Steinberg varieties that interpolates between the Steinberg variety of a reductive, complex algebraic group and its nilpotent cone in terms of the extended affine Hecke algebra…

We establish ring isomorphisms between quantum Grothendieck rings of certain remarkable monoidal categories of finite-dimensional representations of quantum affine algebras of types $A_{2n-1}^{(1)}$ and $B_n^{(1)}$. Our proof relies in part…

A Coxeter group is said to be \emph{$\mathbf{a}(2)$-finite} if it has finitely many elements of $\mathbf{a}$-value 2 in the sense of Lusztig. In this paper, we give explicit combinatorial descriptions of the left, right, and two-sided…

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…

According to an old result of Sch\"utzenberger, the involutions in a given two-sided cell of the symmetric group $\SG_n$ are all conjugate. In this paper, we study possible generalisations of this property to other types of Coxeter groups.…

We establish a direct connection between the representation theories of Lie algebras and Lie superalgebras (of type A) via Fock space reformulations of their Kazhdan-Lusztig theories. As a consequence, the characters of finite-dimensional…

George Lusztig conjectured that asymptotic affine Hecke algebra of a simply connected group can be explicitly described in terms of convolution algebras. Main Theorem of this note (which is a continuation of RT/0010089) is a weak version of…

Graded Hecke algebras can be constructed in terms of equivariant cohomology and constructible sheaves on nilpotent cones. In earlier work, their standard modules and their irreducible modules where realized with such geometric methods. We…

Kazhdan and Lusztig proved that Vogan classes are unions of cells in the equal parameter case. We extend this result in the unequal parameter case.

More than 10 years ago, Dipper, James and Murphy developped the theory of Specht modules for Hecke algebras of type $B\_n$. More recently, using Lusztig's a-function, Geck and Rouquier showed how to obtain parametrisations of the…

Let $W$ be a finite Coxeter group and $L$ be a weight function on $W$ in the sense of Lusztig. We have recently introduced a pre-order relation $\preceq_L$ on the set of irreducible characters of $W$ which extends Lusztig's definition of…

The aim of this work is to prove a conjecture related to the Combinatorial Invariance Conjecture of Kazhdan-Lusztig polynomials, in the parabolic setting, for lower intervals in every arbitrary Coxeter group. This result improves and…

Kazhdan-Lusztig polynomials are important and mysterious objects in representation theory. Here we present a new formula for their computation for symmetric groups based on the Bruhat graph. Our approach suggests a solution to the…

In this paper, we propose a conjectural formula for the order of the poles of intertwining operators in the context of the representation theory of general linear groups over $p$-adic fields. More specifically, we conjecturally relate the…

We establish combinatorial and inductive formulas for Kazhdan-Lusztig polynomials associated to covexillary elements in classical types, extending results of Boe, Lascoux-Sch\"{u}tzenberger, Sankaran-Vanchinathan, and Zelevinsky for…

We show that the Kazhdan-Lusztig basis elements $C_w$ of the Hecke algebra of the symmetric group, when $w \in S_n$ corresponds to a Schubert subvariety of a Grassmann variety, can be written as a product of factors of the form…

We revisit Haiman's conjecture on the relations between characters of Kazdhan-Lusztig basis elements of the Hecke algebra over the symmetric group. The conjecture asserts that, for purposes of character evaluation, any Kazhdan-Lusztig basis…

To any element of a connected, simply connected, semisimple complex algebraic group G and a choice of an element of the corresponding Weyl group there is an associated Lusztig variety. When the element of G is regular semisimple, the…

We give a $K$-theoretic realization of all affine Hecke algebras with two unequal parameters including exceptional types. This extends the celebrated work of Kazhdan and Lusztig, who gave a $K$-theoretic realization of affine Hecke algebras…

We give an explicit expression for the central elements of affine Hecke algebras of type A in the Coxeter presentation, in terms of (parabolic) affine Kazhdan-Lusztig polynomials. Our approach is based on a version of quantum affine…