Journal of Algebraic Combinatorics

, Volume 20, Issue 1, pp 33–53

Bruhat-Chevalley Order in Reductive Monoids

  • Mohan S. Putcha

Abstract

Let M be a reductive monoid with unit group G. Let Λ denote the idempotent cross-section of the G × G-orbits on M. If W is the Weyl group of G and e, f ∈ Λ with ef, 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 Borel subgroup B0 of G0, we show that the poset of B0 × B0-orbits of X (with respect to Zariski closure inclusion) is Eulerian.

reductive monoid Renner monoid Bruhat-Chevalley order projections 

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Copyright information

© Kluwer Academic Publishers 2004

Authors and Affiliations

  • Mohan S. Putcha
    • 1
  1. 1.Department of MathematicsNorth Carolina State UniversityRaleigh

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