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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 the Schiitzenberger representations of M, we construct left and right induced characters 9~ and 9~ of the unit group G of M. We show that the sum of suitable intertwining(More)
The purpose of this paper is to extend to monoids the work of Björner, Wachs and Proctor on the shellability of the Bruhat-Chevalley order on Weyl groups. Let M be a reductive monoid with unit group G, Borel subgroup B and Weyl group W . We study the partially ordered set of B×Borbits (with respect to Zariski closure inclusion) within a G × G-orbit of M .(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. We use this to: 1. find a description of the irreducible representations of H, 2. find an explicit isomorphism between H and the monoid algebra of the Renner monoid(More)
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(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 the unit group G of M . When M has a unique non-trivial minimal or maximal G×G-orbit, we find a precise description of the irreducible components of Mnil via the(More)
By the well-known result of A. H. Clifford, any band of left Archimedean semigroups is a semilattice of matrices (rectangular bands) of left Archimedean semigroups. The converse of this assertion don't hold, i.e. the class of semilattices of matrices of left Archimedean semigroups is larger than the class of bands of left Archimedean semigroups. In this(More)