Pascal's triangle and word bases for blob algebra ideals
We give an elementary proof of isomorphism of the blob (diagram) algebra and the corresponding extended Temperley-Lieb algebra (defined by presentation).
math.RT↗
arXiv subjects
P P Martin
Publications and source records attributed to P P Martin.
A faithful tensor space representation for the blob algebra
We show that a certain tensor space representation of the blob algebra (an affine Hecke algebra quotient) is faithful.
math.RT↗
Virtual algebraic Lie theory: Tilting modules and Ringel duals for blob algebras
We construct a representation of the blob algebra over a ring allowing base change to every interesting (i.e. non--semisimple) specialisation which, in quasihereditary specialisations, passes to a full tilting module.
math.RT↗
Ramified partition algebras
We introduce the ramified partition algebra, which is a physically motivated and natural generalization of the partition algebra. We investigate its representation theory and demonstrate quasi--heredity under certain conditions. Under these conditions we determine an index set for simple modules and construct standard modules with this index set. We construct tensor space representations of certain non--semisimple specializations, and show how to use these to build clock model transfer matrices in arbitrary physical dimensions.
math.RT↗
Hecke algebraic approach to the reflection equation for spin chains
We use the structural similarity of certain Coxeter Artin Systems to the Yang--Baxter and Reflection Equations to convert representations of these systems into new solutions of the Reflection Equation. We construct certain Bethe ansatz states for these solutions, using a parameterisation suggested by abstract representation theory.
hep-th↗