Representation theory of towers of recollement: theory notes and examples

A. G. Cox, P. P. Martin, A. E. Parker and C. Xi.

Abstract

We give an axiomatic framework for studying the representation theory of towers of algebras. We introduce a new class of algebras, contour algebras, generalising (and interpolating between) blob algebras and cyclotomic Temperley-Lieb algebras. We demonstrate the utility of our formalism by applying it to this class.