Bruhat-Chevalley Order in Reductive Monoids

  • Authors:

  • Mohan S. Putcha

  • Affiliations:

  • Department of Mathematics, Box 8205, North Carolina State University, Raleigh, NC 27695-8205

  • Venue:
  • Journal of Algebraic Combinatorics: An International Journal
  • Year:
  • 2004

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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 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 Borel subgroup B0 of G0, we show that the poset of B0 × B0-orbits of X (with respect to Zariski closure inclusion) is Eulerian.