Towers of recollement and bases for diagram algebras: planar diagrams and a little beyond
The recollement approach to the representation theory of sequences of algebras is extended to pass basis information directly through the globalisation functor. The method is hence adapted to treat sequences that are not necessarily towers by inclusion, such as symplectic blob algebras (diagram algebra quotients of the affine-C Hecke algebras). We find a new set of functors interrelating module categories of ordinary blob algebras (one-boundary Temperley-Lieb algebras, themselves affine Hecke algebra quotients). We show that these functors generalise to determine the structure of symplectic blob algebras, and hence of certain two-boundary Temperley-Lieb algebras arising in Statistical Mechanics.
This page last modified by Alison Parker on Wed Sep 5 2007