arXiv subjects
Publications and source records attributed to A. E. Parker.
We determine the semisimplicity criterion for even partition algebras over the complex field. Specifically we prove that the even/2-tonal partition algebras $P_n^2(δ)$ over $\mathbb{C}$ are semisimple for all $n$ if and only if parameter $δ\not\in \mathbb{N}_0$ .
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 $A$.