Bruhat-Chevalley Order in Reductive Monoids
نویسنده
چکیده
Let M be a reductive monoid with unit group G. Let denote the idempotent cross-section of the G × G-orbits on M . If W is the Weyl group of G and e, f ∈ 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.
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