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- Mohan S. Putcha, MOHAN S. Pl'TCHA
- 1996

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)

- Mohan S. Putcha
- 2001

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)

- Mohan S. Putcha
- 1997

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)

In this paper we study the orbit structure of semisimple algebraic monoids with exactly two nonzero minimal G×G-orbits. The case of one minimal orbit was solved earlier by the authors. The key notion for reductive monoids is the type map λ, which is the monoid notion of the Dynkin diagram. It is the ultimate combinatorial invariant of a reductive monoid. To… (More)

- Mohan S. Putcha
- 2004

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)

- Mohan S. Putcha
- 2004

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)

- ALGEBRAIC MONOIDS, Mohan S. Putcha
- 2010

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)

- Mohan S. Putcha
- Discrete Mathematics
- 1975

- Mohan S. Putcha
- IJAC
- 2001