The variety of J-trivial monoids does not enjoy the semi-simplicity of groups, but has other properties which make their representation theory approachable and inherently combinatorial. I will describe these combinatorics, and also present important examples of some J-trivial monoids, including the zero-Hecke monoid, the monoid of regressive order-preserving functions on a poset, and the upper-unitriangular matrices over the boolean semiring.
Combinatorial Representation Theory of J-Trivial Monoids
Combinatorial Representation Theory of J-Trivial Monoids