Bruhat-Chevalley Order in Reductive Monoids

Bruhat-Chevalley Order in Reductive Monoids

Let M be a reductive monoid with unit group G. Let denote the idempotent cross-section of the G × G-orbits on M . If W is the Weyl group of G and e, f ∈ with e ≤ f , we introduce a projection map from WeW to WfW. We use these projection maps to obtain a new description of the Bruhat-Chevalley order on the Renner monoid of M . For the canonical compactification X of a semisimple group G0 with Bo...

Fine Bruhat Intersections for Reductive Monoids

Taylor, Dewey Terese. Fine Bruhat Intersections for Reductive Monoids. (Under the direction of Mohan S. Putcha.) Fine Bruhat intersections for reductive groups have been studied by several authors in connection with Kazhdan-Lusztig theory, canonical bases and Lie Theory. The purpose of this thesis is to study the analogous intersections for reductive monoids. We determine the conditions under w...

Shellability in Reductive Monoids

The purpose of this paper is to extend to monoids the work of Björner, Wachs and Proctor on the shellability of the Bruhat-Chevalley order on Weyl groups. Let M be a reductive monoid with unit group G, Borel subgroup B and Weyl group W . We study the partially ordered set of B×Borbits (with respect to Zariski closure inclusion) within a G × G-orbit of M . This is the same as studying a W ×W -or...

Intersection of Conjugacy Classes with Bruhat Cells in Chevalley Groups

Let (G,B,N, S) be a Tits system. Some aspects of intersections of conjugacy classes ofG with Bruhat cellsBẇB have been investigated by several authors (see e.g., [St1], [K], [V] and [VS]). Here w ∈ W = N/(B ∩N) and ẇ ∈ N is a preimage of w with respect to the natural surjection N → W . In particular, it is desirable to learn how a conjugacy class C of G is related to those conjugacy classes Cw ...

Bases for the Bruhat{chevalley Order on All Nite Coxeter Groups