In this paper we study the complex representations of arbitrary finite monoids M. Let 9 be an irreducible character of a maximal subgroup (or Schiitzenberger group) of M. Related to theâ€¦ (More)

The purpose of this paper is to extend to monoids the work of BjÃ¶rner, Wachs and Proctor on the shellability of the Bruhat-Chevalley order on Weyl groups. Let M be a reductive monoid with unit groupâ€¦ (More)

Let M be a finite monoid of Lie type (these are the finite analogues of linear algebraic monoids) with group of units G . The multiplicative semigroup ^AfF), where F is a finite field, is aâ€¦ (More)

This paper concerns the monoid Hecke algebras H introduced by Louis Solomon. We determine explicitly the unities of the orbit algebras associated with the two-sided action of the Weyl group W . Weâ€¦ (More)

In this paper we study the orbit structure of semisimple algebraic monoids with exactly two nonzero minimal GÃ—G-orbits. The case of one minimal orbit was solved earlier by the authors. The key notionâ€¦ (More)

In this paper we study the variety Mnil of nilpotent elements of a reductive monoid M . In general this variety has a completely different structure than the variety Guni of unipotent elements of theâ€¦ (More)

Let M be a reductive monoid with unit group G. Let denote the idempotent cross-section of the G Ã— G-orbits on M . If W is the Weyl group of G and e, f âˆˆ with e â‰¤ f , we introduce a projection mapâ€¦ (More)