Mohan S. Putcha

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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)
Let R be a ring and let N denote the set of nilpotent elements of R. Let n be a nonnegative integer. The ring R is called a @ -ring if the number n of elements in R which are not in N is at most n. The following theorem is proved: If R is a @ -ring, then R is nil or R is finite. Conversely, if R n is a nil ring or a finite ring, then R is a 8 -ring for some(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)
Using some results on linear algebraic groups, we show that every connected linear algebraic semlgroup S contains a closed, connected dlagonallzable subsemlgroup T with zero such that E(T) intersects each regular J-class of S. It is also shown that the lattice (E(T),<) is isomorphic to the lattice of faces of a n rational polytope in some Using these(More)
In this paper we study connected regular linear algebraic monoids. If <¡>: G0 -» GL(«, K) is a representation of a reductive group G0, then the Zariski closure of K(f>(G0) in Jf„(K) is a connected regular linear algebraic monoid with zero. In §2 we study abstract semigroup theoretic properties of a connected regular linear algebraic monoid with zero. We(More)