Related papers: Lusztig $\mathbf{a}$-functions for quasiparabolic …

We give an easy diagrammatical description of the parabolic Kazhdan-Lusztig polynomials for the Weyl group $W_n$ of type $D_n$ with parabolic subgroup of type $A_n$ and consequently an explicit counting formula for the dimension of the…

We prove that, for any choice of parameters, the Kazhdan-Lusztig cells of a Weyl group of type $B$ are unions of combinatorial cells (defined using the domino insertion algorithm).

We extend the techniques in arXiv:2209.08865(1) to the non-simply-laced situation, and calculate explicit special values of parabolic affine inverse Kazhdan-Lusztig polynomials for subregular nilpotent orbits. We thus obtain explicit…

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.

Computations in small Coxeter groups or dihedral groups suggest that the partition into Kazhdan-Lusztig cells with unequal parameters should obey to some semicontinuity phenomenon (as the parameters vary). The aim of this paper is to…

We present a unified parametrisation of $\ell$-blocks of quasi-simple finite groups of Lie type in non-defining characteristic via Lusztig's induction functor in terms of $e$-Jordan-cuspidal pairs and $e$-Jordan quasi-central cuspidal…

We give a new expression for the inner product of two kernel functions associated to a cusp form. Among other applications, it yields an extension of a formula of Kohnen and Zagier, and another proof of Manin's Periods Theorem. Cohen's…

In [Lu6] Lusztig defined a certain algebra $H,$ which is a direct sum of various algebras $H_{\mathfrak{o}}.$ We establish an explicit algebra isomorphism between each algebra $H_{\mathfrak{o}}$ and some matrix algebra with coefficients in…

Let "$\leq_L$" be the Kazhdan-Lusztig left cell preorder on the symmetric group $S_n$. Let $w\mapsto (P(w),Q(w))$ be the Robinson-Schensted-Knuth correspondence between $S_n$ and the set of standard tableaux with the same shapes. We prove…

In this paper we introduced an arithmetic graph function which associates with every group G the directed graph whose vertices corresponds to the divisors of |G|. With the help of such functions we introduced arithmetic graphs of classes of…

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 propose the categorification of the algebraic analysis as the Leibniz 3-category given by generators and relations, including the Leibniz 3-cell relation. The Leibniz category offers the `most general' `(co-)derivation' 3-cell. We…

We construct two categorifications of the Lusztig--Vogan module associated to a real reductive algebraic group. The first categorification is given by semisimple complexes in an equivariant derived category, and the second is constructed as…

Let $\breve{G}$ be a loop group and $\tilde W$ be its Iwahori-Weyl group. The affine Lusztig variety $Y_w(\gamma)$ describes the intersection of the Bruhat cell $\mathcal{I} \dot{w} \mathcal{I}$ for $w \in \tilde W$ with the conjugacy class…

Let $\mathfrak{g}$ be the Lie algebra $\mathfrak{sl}(n,\mathbb{C})$. Its Weyl group is the symmetric group $S_n$. In this paper, we want to describe some Kazhdan-Lusztig right cells containing smooth elements which parameterize the smooth…

Let G be a semisimple algebraic group over an algebraically closed field of characteristic p>0, and let g be its Lie algebra. The crucial Lie algebra representations to understand are those associated with the reduced enveloping algebra…

The totally nonnegative part of a partial flag variety G/P is known to have a decomposition into semi-algebraic cells. We show that the closure of a cell is again a union of cells and give a combinatorial description of the closure…

The paper constructs new Hecke endomorphism algebras with a stratified structure. A novel feature of the proof is to approach difficult Ext^1 vanishing conditions by building entire exact category structures in which the analogous vanishing…

In relation to Kostant's problem for simple highest weight modules over the general linear Lie algebra, we prove a persistence result for Kostant negative consecutive patterns. Inspired by it, we introduce the notion of a Kostant cuspidal…

In this paper, we define the KW cell system on a graph $\Gamma$, depending on parameters $N\in \mathbb{N}$, $q$ a root of unity, and $\omega$ an $N$-th root of unity. This is a polynomial system of equations depending on $\Gamma$ and the…