Effective representations of Hecke-Kiselman monoids of type A

2012/05/03 by Forsberg, Love
#FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1205.0676

Abstract

We prove effectiveness of certain representations of Hecke-Kiselman monoids of type A constructed by Ganyushkin and Mazorchuk and also construct further classes of effective representations for these monoids. As a consequence the effective dimension of monoids of type A is determined. We also show that odd Fibonacci numbers appear as the cardinality of certain bipartite HK-monoids and count the number of multiplicity free elements in any HK-monoid of type A.

Related

• The word problem for Hecke--Kiselman monoids of type A_n and \widetildeA_n
• The Finite Basis Problem for Kiselman Monoids
• Irreducible representations of Hecke-Kiselman monoids
• Representations of A-type Hecke algebras
• The representation theory of the increasing monoid