Abstract:
In this thesis, to each Borel-de Siebenthal discrete series representation of G(0), the author would associate a holomorphic discrete series representation of K*(0). The main aim of the thesis is to compare the restrictions to the compact subgroup L(0) of G(0) which is also a maximal compact subgroup of K*(0), of a Borel-de Siebenthal discrete series representation and its associated holomorphic discrete series representation under certain conditions. The question, "Does there exist common L(0) types between a Borel-de Siebenthal discrete series representation and its associated holomorphic discrete series representation?", is addressed in this thesis and it is completely settled in the so called quaternionic case.
