相关论文: Classification of weak Bruhat interval modules of …

The purpose of this paper is to provide a unified method for dealing with various 0-Hecke modules constructed using tableaux so far. To do this, we assign a $0$-Hecke module to each left weak Bruhat interval, called a weak Bruhat interval…

We extend the recently-introduced weak Bruhat interval modules of the type A $0$-Hecke algebra to all finite Coxeter types. We determine, in a type-independent manner, structural properties for certain general families of these modules,…

We study the appearance of notable interval structures -- lattices, modular lattices, distributive lattices, and boolean lattices -- in both the Bruhat and weak orders of Coxeter groups. We collect and expand upon known results for…

We study Soergel modules for arbitrary Coxeter groups. For infinite Coxeter groups, we show that the homomorphisms between Soergel modules are in general more than those coming from morphisms of Soergel bimodules. This result provides a…

We classify all quotients $W/W_J$ up to isomorphism in Bruhat order, with $(W,S)$ a Coxeter system and $W_J$ a parabolic subgroup of $W$. In particular, the non-trivial isomorphisms fall into a small number of cases which are highly…

We extend the weak Bruhat order of a finite Coxeter group to the set of its coclasses, modulo parabolic standard subgroups. We use this order to describe associative algebra structures on the vector spaces spanned by the faces of…

In this paper we present the general theory of cleft extensions for a cocommutative weak Hopf algebra $H$. For a weak left $H$-module algebra we obtain a bijective correspondence between the isomorphisms classes of $H$-cleft extensions…

The number of Bruhat intervals in Coxeter groups is finite, and for the first few lengths, the intervals were described up to an isomorphism by A. Hultman using the correspondence between Bruhat intervals and cell decompositions of a 2d…

Given a Coxeter group $W$ with Coxeter system $(W,S)$, where $S$ is finite. We provide a complete characterization of Boolean intervals in the weak order of $W$ uniformly for all Coxeter groups in terms of independent sets of the Coxeter…

For affine Weyl groups and elements associated to dominant coweights, we present a convex geometry formula for the size of the corresponding lower Bruhat intervals. Extensive computer calculations for these groups have led us to believe…

We define a class of partial orders on a Coxeter group associated with sets of reflections. In special cases, these lie between the left weak order and the Bruhat order. We prove that these posets are graded by the length function and that…

We begin by deriving an action of the 0-Hecke algebra on standard reverse composition tableaux and use it to discover 0-Hecke modules whose quasisymmetric characteristics are the natural refinements of Schur functions known as…

Let $\mathrm{Int}(n)$ denote the set of nonempty left weak Bruhat intervals in the symmetric group $\mathfrak{S}_n$. We investigate the equivalence relation $\overset{D}{\simeq}$ on $\mathrm{Int}(n)$, where $I \overset{D}{\simeq} J$ if and…

We provide an algorithm to construct a multicomplex for any lower Bruhat interval of $F_4$, such that its rank--generating function equals that of the Bruhat interval. For Weyl groups, it is always possible to find such a multicomplex…

We study Bruhat intervals in affine Weyl groups by viewing them as regions of alcoves. In type $\widetilde{A}_2$ we show that each interval coincides with a generalized permutohedron minus a star-shaped polygon, and we prove a subtler…

In certain finite posets, the expected down-degree of their elements is the same whether computed with respect to either the uniform distribution or the distribution weighting an element by the number of maximal chains passing through it.…

Let (W,S) be a crystallographic Coxeter group (this includes all finite and affine Weyl groups), and J a subset of S. Let $W^J$ denote the set of minimal coset representatives modulo the parabolic subgroup $W_J$. For w in $W^J$, let…

Recently, Wang and the second author constructed a bar involution and canonical basis for a quasi-permutation module of the Hecke algebra associated to a type B Weyl group $W$, where the basis is parameterized by left cosets of a…

We show that any lower Bruhat interval in a Coxeter group is a disjoint union of certain two-sided cosets as a consequence of Lifting Property and Subword Property. Furthermore, we describe these details in terms of Bruhat graphs, graded…

The reducible Specht modules for the Hecke algebra $\mathcal{H}_{\mathbb{F},q}(\mathfrak{S}_n)$ have been classified except when $q=-1$. We prove one half of a conjecture which we believe classifies the reducible Specht modules when $q=-1$…