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.