Generic Hecke algebra for Renner monoids

A Note on Renner Monoids

We extend the result obtained in [3] to every Renner monoid: we provide Renner monoids with a monoid presentation and we introduce a length function which extends the Coxeter length function and which behaves nicely.

A Generic Algebra Associated to Certain Hecke Algebras

We initiate the systematic study of endomorphism algebras of permutation modules and show they are obtainable by a descent from a certain generic Hecke algebra, infinite-dimensional in general, coming from the universal enveloping algebra of gl n (or sln). The endomorphism algebras and the generic algebras are cellular (in the latter case, of profinite type in the sense of R.M. Green). We give ...

. Renner Linear Algebraic Monoids SPIN – Monograph – January 12 , 2005

On Kiselman Quotients of 0-hecke Monoids

Combining the definition of 0-Hecke monoids with that of Kiselman semigroups, we define what we call Kiselman quotients of 0-Hecke monoids associated with simply laced Dynkin diagrams. We classify these monoids up to isomorphism, determine their idempotents and show that they are J -trivial. For type A we show that Catalan numbers appear as the maximal cardinality of our monoids, in which case ...

The affine Hecke algebra

1 The affine Hecke algebra 1.1 The alcove walk algebra Fix notations for the Weyl group W , the extended affine Weyl group W , and their action on Ω × h * R as in Section 2. Label the walls of the alcoves so that the fundamental alcove has walls labeled 0, 1,. .. , n and the labeling is W-equivariant (see the picture in (2.12)). The periodic orientation is the orientation of the walls of the al...