Related papers: Flip Combinatorial Invariance and Weyl groups

For each infinite series of the classical Lie groups of type B,C or D, we introduce a family of polynomials parametrized by the elements of the corresponding Weyl group of infinite rank. These polynomials represent the Schubert classes in…

We present a new class of extended affine Weyl groups $\widetilde{W}^{(k,k+1)}(A_l)$ for $1\leq k <l$ and obtain an analogue of Chevalley-type theorem for their invariants. We further show the existence of Frobenius manifold structures on…

We classify all invariants of the functor $I^n$ (powers of the fundamental ideal of the Witt ring) with values in $A$, that it to say functions $I^n(K)\rightarrow A(K)$ compatible with field extensions, in the cases where $A(K)=W(K)$ is the…

The paper [GLZ] "L-functions of Carlitz modules, resultantal varieties and rooted binary trees" is devoted to a description of some resultantal varieties related to L-functions of Carlitz modules. It contains a conjecture that some of these…

We define a family of universal finite-dimensional highest weight modules for affine Lie algebras, we call these Weyl modules. We conjecture that these are the classical limits of the irreducible finite--dimensional representations of the…

We show that except in several cases conjugacy classes of classical Weyl groups $W(B_n)$ and $W(D_n)$ are of type {\rm D}. We prove that except in three cases Nichols algebras of irreducible Yetter-Drinfeld ({\rm YD} in short )modules over…

Soergel bimodules are certain bimodules over polynomial algebras, associated with Coxeter groups, and introduced by Soergel in the 1990's while studying the category O of complex semisimple Lie algebras. Even though their definition is…

It is shown that except in three cases conjugacy classes of classical Weyl groups $W(B_{n})$ and $W(D_{n})$ are of type ${\rm D}$. This proves that Nichols algebras of irreducible Yetter-Drinfeld modules over the classical Weyl groups…

For integral weights $\lambda$ and $\mu$ of a classical simple Lie algebra $\mathfrak{g}$, Kostant's weight multiplicity formula gives the multiplicity of the weight $\mu$ in the irreducible representation with highest weight $\lambda$,…

Let k be an algebraically closed field of characteristic p>2. We compute the Weyl filtration multiplicities in indecomposable tilting modules and the decomposition numbers for the symplectic group over k in terms of cap-curl diagrams under…

We show a precise formula, in the form of a monomial, for certain families of parabolic Kazhdan-Lusztig polynomials of the symmetric group. The proof stems from results of Lapid-Minguez on irreducibility of products in the…

Let $(W, I)$ be a finite Coxeter group. In the case where $W$ is a Weyl group, Berenstein and Kazhdan in \cite{BK} constructed a monoid structure on the set of all subsets of $I$ using unipotent $\chi$-linear bicrystals. In this paper, we…

We describe an algorithm which pattern embeds, in the sense of Woo-Yong, any Bruhat interval of a symmetric group into an interval whose extremes lie in the same right Kazhdan-Lusztig cell. This apparently harmless fact has applications in…

We find the generators of the fields of invariants of the coadjoint action of the unitriangular group on the basic varieties and basic cells. It is proved that the transcendental degree of the field of invariants on a basic cell coincides…

In this paper we prove the Kazhdan-Lusztig type character formula for irreducible highest weight modules with positive rational highest weights over symmetrizable Kac-Moody Lie algebras.

We develop the $L$-functions ratios conjecture with one shift in the numerator and denominator in certain ranges for the family of quadratic twist of modular $L$-functions using multiple Dirichlet series under the generalized Riemann…

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…

A classic result of Conway and Coxeter on frieze patterns has been generalized to a bijection between $p$-angulations of regular polygons and frieze patterns of type $\Lambda_p$. One of the features of Conway-Coxeter theory is a…

We compute the expansion of the cohomology class of the permutahedral variety in the basis of Schubert classes. The resulting structure constants $a_w$ are expressed as a sum of \emph{normalized} mixed Eulerian numbers indexed naturally by…

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…