Distinction and gamma factors at 1/2: Supercuspidal case

Abstract

Let F be a non-archimedean local field of characteristic $\not=$2 and E a quadratic extension of F. We say that an irreducible admissible representation $\pi$ of $GL(r,E)$ is distinguished if there exists a linear form L on the space of $\pi$ which is invariant under $GL(r,F).$ In the thesis, we study the relation of distinguished representations with the values of gamma factors at ${1\over2}.$ Here the gamma factors are the functions appearing as ratios of relevant integrals in the functional equations. Because we make use of extensive calculations, we restrict ourselves to supercuspidal representations. We think these results will hold also for tempered representations.