Shellability in Reductive Monoids
نویسنده
چکیده
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 -orbit in the Renner monoid R. Such an orbit is the retract of a ‘universal orbit’, which is shown to be lexicograhically shellable in the sense of Björner and Wachs.
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