Eulerian central limit theorems and Carlitz identities in positive elements of classical Weyl groups

Minuscule Elements of Weyl Groups

Excedances in classical and affine Weyl groups

Based on the notion of colored and absolute excedances introduced by Bagno and Garber we give an analogue of the derangement polynomials. We obtain some basic properties of these polynomials. Moreover, we define an excedance statistic for the affine Weyl groups of type B̃n, C̃n and D̃n and determine the generating functions of their distributions. This paper is inspired by one of Clark and Ehrenbo...

Fully Commutative Elements in the Weyl and Affine Weyl Groups

Let W be a Weyl or affine Weyl group and let Wc be the set of fully commutative elements in W . We associate each w ∈ Wc to a digraph G(w). By using G(w), we give a graph-theoretic description for Lusztig’s a-function on Wc and describe explicitly all the distinguished involutions of W . The results verify two conjectures in our case: one was proposed by myself in [15, Conjecture 8.10] and the ...

Reflection decompositions in the classical Weyl groups

In this paper, we present formulas for the number of decompositions of elements of the Weyl groups of type A., D. and B, as products of a number of reflections that is not necessarily minimal. For this purpose, we consider the poset of conjugacy classes of W introduced in B6dard and Goupil (1992) for the symmetric group. This poset describes the action of the set of reflections of a reflection ...

role of cultural iran in promotion of multilaieralism in central asia and caucasus

cultural iran is a scope that is more extended than the political territories of iran as a political unit. this concept means that cultural geography(mehdi moghanlo-1383-1) of iran is greater than its political geography which, according to history, has a long history extending west-east from kandahar to the euphrates and north-south from the persian gulf to the caucasus including transoxiana a...