Abstract
0. Introduction. The purpose of this paper is to continue the study of B×B orbits on a reductive monoidM . This was first taken up systematically by the author in [9], where several basic properties analogous to the case of groups were established. The B×B orbits were identified with a finite monoid R, defined in terms of the normalizer of a maximal torus, and a direct analysis of these orbits led to an extension of Tits’ axiom “ρBr ⊆ BrB ∪ BρrB” to the case of reductive monoids. However, there is more to this axiom when dealing with monoids. Obviously,
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