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 representationsof a p adic group This thesis is divided into two parts In the local Langlandscorrespondence LLC irreducible representations of the group G F of F points of areductive group G defined over a non archimedean local field F are expected to beparametrized by arithmetic objects called Langlands parameters in a natural way Onecan attach a numerical invariant namely the 8216 depth 8217 to each side of LLC We will showthat for a wildly ramified induced torus in general the depth is not preserved under LLCfor 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 seriesHecke algebra newline newline