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Shellability in reductive monoids

Author: Mohan S. Putcha
Journal: Trans. Amer. Math. Soc. 354 (2002), 413-426
MSC (2000): Primary 20G99, 20M99, 06A07
Published electronically: August 30, 2001
MathSciNet review: 1859281
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Abstract: 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 $B\times B$-orbits (with respect to Zariski closure inclusion) within a $G\times G$-orbit of $M$. This is the same as studying a $W\times W$-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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Additional Information

Mohan S. Putcha
Affiliation: Department of Mathematics, North Carolina State University, Raleigh, North Carolina 27695-8205

Received by editor(s): November 24, 1999
Received by editor(s) in revised form: November 6, 2000
Published electronically: August 30, 2001
Article copyright: © Copyright 2001 American Mathematical Society

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