Some tits systems with affine Weyl groups in Chevalley groups over Dedekind domains

Chevalley Groups over Commutative Rings

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...

Left Cells in Affine Weyl Groups

We prove a property of left cells in certain crystallographic groups W , by which we formulate an algorithm to find a representative set of left cells of W in any given two-sided cell. As an illustration, we make some applications of this algorithm to the case where W is the affine Weyl group of type e F4. The cells of affine Weyl groups W , as defined by Kazhdan and Lusztig in [6], have been d...

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 ...

Affine Weyl Groups as Infinite Permutations

We present a unified theory for permutation models of all the infinite families of finite and affine Weyl groups, including interpretations of the length function and the weak order. We also give new combinatorial proofs of Bott’s formula (in the refined version of Macdonald) for the Poincaré series of these affine Weyl groups. 1991 Mathematics Subject Classification. primary 20B35; secondary 0...