On the blob algebra and a Deguchi-Martin quotient of the Hecke algebra

In this thesis, we investigate the representation theory of diagram algebras. We focus on the representation theory of the blob algebra bn and a certain quotient of Hecke algebra type A which is called Deguchi-Martin quotient, HPM n. In particular, this research concerns the semisimple case of these algebras. We use some of the combinatorial results to show that there is a bijection between the canonical basis of the cell modules of the blob algebra bn−1 and the Deguchi-Martin quotient of the Hecke Algebra HPM n. Furthermore, we show that these algebras are isomorphic for n = 2 and n = 3 at a certain value of parameter m.