This thesis is split into two main themes, connected loosely by the main results concerning symmetric functions and the combinatorial representation theory of the symmetric groups. In part A, we shall consider almost monomial groups -- a class of groups defined by Andrew Booker related to Artin L-functions and the Riemann hypothesis. We will first explore some of the properties of these groups, and then, as a main result, show that the symmetric groups are almost monomial. We shall also see that certain general linear groups are also almost monomial and discuss some open problems.In part B, we extend recent results by Chuang and Tan, and Leclerc and Miyachi concerning the Morita equivalence of the Rouquier block of Symmetric group and Iwahori-Hecke algebras to the principal block of a certain wreath product. We shall derive a combinatorial formula for the transition matrix between the canonical bases and standard bases of higher-level Fock spaces. This will, in turn, give the decomposition numbers for Ariki-Koike algebras in characteristic zero.
|Date of Award||2011|
- The University of Bristol
|Supervisor||Jeremy C Rickard (Supervisor)|