Typical representations for GLn(F)

Abstract

In this thesis we classify typical representations for certain non-cuspidal Bernstein components of GL_n over a non-Archimedean local field. Following the work of Henniart in the case of GL_2 and Paskunas for the cuspidal Bernstein components, we classify typical representations for Bernstein components of level-zero for GL_n for n ≥ 3, principal series components, components with Levi subgroup of the form (n, 1) for n > 1 and certain components with Levi subgroup of the form (2, 2). Each of the above component is treated in a separate chapter. The classification uses the theory of types developed by Bushnell and Kutzko in a significant way. We will give the classification in terms of Bushnell-Kutzko types for a given inertial class.