On quasi-heredity and cell module homomorphisms in the symplectic blob algebra

TL;DR

This paper advances the understanding of the symplectic blob algebra's representation theory by constructing homomorphisms between cell modules and identifying minimal posets for its quasi-hereditary structure.

Contribution

It introduces new families of homomorphisms between cell modules and determines the minimal poset structure for the algebra.

Findings

Constructed four large families of homomorphisms

Identified a large family of non-semisimple specialisations

Determined the minimal poset for the algebra

Abstract

This paper reports key advances in the study of the representation theory of the symplectic blob algebra. For suitable specialisations of the parameters we construct four large families of homomorphisms between cell modules. We hence find a large family of non-semisimple specialisations. We find a minimal poset (i.e. least number of relations) for the symplectic blob as a quasi-hereditary algebra.