Abstract:
The main theme of the thesis is the study of the depth and genericity of representations
of a p-adic group. This thesis is divided into two parts. In the local Langlands
correspondence(LLC), irreducible representations of the group G(F) of F-points of a
reductive group G defined over a non-archimedean local field F are expected to be
parametrized by arithmetic objects called Langlands parameters in a natural way. One
can attach a numerical invariant, namely the ‘depth’ to each side of LLC. We will show
that for a wildly ramified induced torus, in general the depth is not preserved under LLC
for tori. In the second part, we will discuss the principal series component of Gelfand-
Graev representations of G(F). We describe the component in terms of principal series
Hecke algebra.
