On the non-generic representation theory of the symplectic blob algebra

Details On the non-generic representation theory of the symplectic blob algebra On the non-generic representation theory of the symplectic blob algebra

2008-07-25

arxiv.org/abs/0807.4101v1

Mathematics

Representation Theory

Scientific paper

This paper reports some advances in the study of the symplectic blob algebra. We find a presentation for this algebra. We find a minimal poset for this as a quasi-hereditary algebra. We discuss how to reduce the number of parameters defining the algebra from 6 to 4 (or even 3) without loss of representation theoretic generality. We then find some non-semisimple specialisations by calculating Gram determinants for certain cell modules (or standard modules) using the good parametrisation defined. We finish by considering some quotients of specialisations of the symplectic blob algebra which are isomorphic to Temperley--Lieb algebras of type $A$.

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