ON THE DEPTH AND GENERICITY OF REPRESENTATIONS of A p-ADIC GROUP.

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.