## Shellability in reductive monoids

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- by Mohan S. Putcha PDF
- Trans. Amer. Math. Soc.
**354**(2002), 413-426 Request permission

## 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.## References

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## Additional Information

**Mohan S. Putcha**- Affiliation: Department of Mathematics, North Carolina State University, Raleigh, North Carolina 27695-8205
- Email: putcha@math.ncsu.edu
- Received by editor(s): November 24, 1999
- Received by editor(s) in revised form: November 6, 2000
- Published electronically: August 30, 2001
- © Copyright 2001 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**354**(2002), 413-426 - MSC (2000): Primary 20G99, 20M99, 06A07
- DOI: https://doi.org/10.1090/S0002-9947-01-02806-9
- MathSciNet review: 1859281