Related papers: Light leaves and Lusztig's conjecture

We present an algebraic framework for the computation of low-degree cohomology of a class of bigraded complexes which arise in Poisson geometry around (pre)symplectic leaves. We also show that this framework can be applied to the more…

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 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…

Let $V$ be a simple vertex operator algebra containing a rank $n$ Heisenberg vertex algebra $H$ and let $C=\text{Com}\left( {H}, {V}\right)$ be the coset of ${H}$ in ${V}$. Assuming that the representation categories of interest are vertex…

We calculate certain ext-groups between modules for a linear algebraic group. The results are in agreement with the Lusztig conjecture.

In the framework of canonical and dual canonical bases of Fock spaces, Brundan in 2003 formulated a Kazhdan-Lusztig type conjecture for the characters of the irreducible and tilting modules in the BGG category for the general linear Lie…

By algebraic group theory, there is a map from the semisimple conjugacy classes of a finite group of Lie type to the conjugacy classes of the Weyl group. Picking a semisimple class uniformly at random yields a probability measure on…

We prove the meridional rank conjecture for twisted links and arborescent links associated to bipartite trees with even weights. These links are substantial generalizations of pretzels and two-bridge links, respectively. Lower bounds on…

We show that Lusztig's conjecture on the irreducible characters of a reductive algebraic group over a field of positive characteristic is equivalent to the generic multiplicity conjecture, which gives a formula for the Jordan-H"older…

For a Coxeter system and a representation $V$ of this Coxeter system, Soergel defined a category which is now called the category of Soergel bimodules and proved that this gives a categorification of the Hecke algebra when $V$ is reflection…

The equivariant Kazhdan-Lusztig polynomial of a braid matroid may be interpreted as the intersection cohomology of a certain partial compactification of the configuration space of n distinct labeled points in the plane, regarded as a graded…

In this paper we complete the proof of the X=K conjecture, that for every family of nonexceptional affine algebras, the graded multiplicities of tensor products of symmetric power Kirillov-Reshetikhin modules known as one-dimensional sums,…

We recast the classical notion of standard tableaux in an alcove-geometric setting and extend these classical ideas to all reduced paths in our geometry. This broader path-perspective is essential for implementing the higher categorical…

In this paper, we introduce and study two cyclotomic level maps defined respectively on the set of nilpotent orbits $\underline{\mathcal{N}}$ in a complex semi-simple Lie algebra $\mathfrak{g}$ and the set of conjugacy classes…

A paper of the first author and Zilke proposed seven combinatorial problems around formulas for the characteristic polynomial and the exponents of an isolated quasihomogeneous singularity. The most important of them was a conjecture on the…

Let $(W,S,L)$ be a weighted Coxeter system and $J$ a subset of $S$, Yin [12] introduced the weighted $W$-graph ideal $E_J$ and the weighted Kazhdan-Lusztig polynomials $ \left \{ P_{x,y} \mid x,y\in E_J\right \}$. In this paper, we study…

We prove the local hard Lefschetz theorem and local Hodge-Riemann bilinear relations for Soergel bimodules. Using results of Soergel and K\"ubel one may deduce an algebraic proof of the Jantzen conjectures. We observe that the Jantzen…

In combinatorial representation theory, Kostant's weight multiplicity formula $m(\lambda,\mu)$ is a tool that provides a means of determining the multiplicity of a weight $\mu$ in the adjoint representation of a simple Lie algebra…

We classify the simple modules for the rational Cherednik algebra that are irreducible when restricted to W, in the case when W is a finite Weyl group. The classification turns out to be closely related to the cuspidal two-sided cells in…

We give a constructive account of the fundamental ingredients of Poisson Lie theory as the basis for a description of the classical double group $D$. The double of a group $G$ has a pointwise decomposition $D\sim G\times G^*$, where $G$ and…