Mathematics – Representation Theory
Scientific paper
2006-10-31
Mathematics
Representation Theory
61 pages
Scientific paper
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 type-$\hati{C}$ Hecke algebras). By carefully reviewing the diagram algebra construction, we find a new set of functors interrelating module categories of ordinary blob algebras (diagram algebra quotients of the type-${B}$ Hecke algebras) at {\em different} values of the algebra parameters. 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. We identify the diagram basis with a cellular basis for each symplectic blob algebra, and prove that these algebras are quasihereditary over a field for almost all parameter choices, and generically semisimple. (That is, we give bases for all cell and standard modules.)
Green Richard M.
Martin Paul
Parker Alison
No associations
LandOfFree
Towers of recollement and bases for diagram algebras: planar diagrams and a little beyond does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Towers of recollement and bases for diagram algebras: planar diagrams and a little beyond, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Towers of recollement and bases for diagram algebras: planar diagrams and a little beyond will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-47524