Parker, AlisonMartin, PaulAlotaibi, Nura2023-09-172023-09-172023-05-11https://hdl.handle.net/20.500.14154/69178In 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.107en-USrepresentation theory of Hecke algebraThesis