Related papers: A new statistic on the hyperoctahedral groups

Arc permutations, which were originally introduced in the study of triangulations and characters, have recently been shown to have interesting combinatorial properties. The first part of this paper continues their study by providing signed…

The concept of descent algebras over a field of characteristic zero is extended to define descent algebras over a field of prime characteristic. Some basic algebraic structure of the latter, including its radical and irreducible modules, is…

Descent polynomials and peak polynomials, which enumerate permutations with given descent and peak sets respectively, have recently received considerable attention. We give several formulas for $q$-analogs of these polynomials which refine…

We construct a categorification of the braid groups associated with Coxeter groups inside the homotopy category of Soergel's bimodules. Classical actions of braid groups on triangulated categories should come from an action of this monoidal…

We define a new statistic $\mathsf{sor}$ on the set of colored permutations $\mathsf{G}_{r,n}$ and prove that it has the same distribution as the length function. For the set of restricted colored permutations corresponding to the…

Let G be a reductive algebraic group over Q, and suppose that Gamma is an arithmetic subgroup of G(R) defined by congruence conditions. A basic problem in arithmetic is to determine the multiplicities of discrete series representations in…

The main result of this paper is a convexity theorem for momentum mappings of certain hamiltonian actions of noncompact semisimple Lie groups. The image is required to fall within a certain open subset D of the (dual of the) Lie algebra,…

Our goal is to find classes of convolution semigroups on Lie groups $G$ that give rise to interesting processes in symmetric spaces $G/K$. The $K$-bi-invariant convolution semigroups are a well-studied example. An appealing direction for…

We establish effective equidistribution theorems, with a polynomial error rate, for orbits of unipotent subgroups in quotients of quasi-split, almost simple Linear algebraic groups of absolute rank 2. As an application, inspired by the…

An introduction to inhomogeneous Poisson groups is given. Poisson inhomogeneous $O(p,q)$ are shown to be coboundary, the generalized classical Yang-Baxter equation having only one-dimensional right hand side. Normal forms of the classical…

For W a finite Coxeter group, a formula is found for the size of W equivalence classes of subsets of a base. The proof is a case-by-case analysis using results and tables of Carter and Orlik/Solomon. As a corollary we obtain an alternating…

We study divergence and thickness for general Coxeter groups $W$. We first characterise linear divergence, and show that if $W$ has superlinear divergence then its divergence is at least quadratic. We then formulate a computable…

The $1/3$-$2/3$ Conjecture, originally formulated in 1968, is one of the best-known open problems in the theory of posets, stating that the balance constant (a quantity determined by the linear extensions) of any non-total order is at least…

We study the Whittaker coefficients of the minimal parabolic Eisenstein series on the $n$-fold cover of the split odd orthogonal group $SO_{2r+1}$. If the degree of the cover is odd, then Beineke, Brubaker and Frechette have conjectured…

Standard high-dimensional factor models assume that the comovements in a large set of variables could be modeled using a small number of latent factors that affect all variables. In many relevant applications in economics and finance,…

We investigate a novel diagrammatic approach to examining strict actions of a Coxeter group or a braid group on a category. This diagrammatic language, which was developed in a series of papers by Elias, Khovanov and Williamson, provides…

We investigate the question of how to compute the cotensor product, and more generally the derived cotensor (i.e., Cotor) groups, of a tensor product of comodules. In particular, we determine the conditions under which there is a…

This paper is devoted to the evaluation of the generating series of the connection coefficients of the double cosets of the hyperoctahedral group. Hanlon, Stanley, Stembridge (1992) showed that this series, indexed by a partition $\nu$,…

A new extension of the major index, defined in terms of Coxeter elements, is introduced. For the classical Weyl groups of type $B$, it is equidistributed with length. For more general wreath products it appears in an explicit formula for…

Let $H$ and $K$ be subgroups of a finite group $G$. Pick $g \in G$ uniformly at random. We study the distribution induced on double cosets. Three examples are treated in detail: 1) $H = K = $ the Borel subgroup in $GL_n(\mathbb{F}_q)$. This…