Invariant Representations of $/Mathrm{Gsp}(2)$ Under Tensor Product with a Quadratic Character

Let $F$ be a number field or a $p$-adic field. The author introduces in Chapter 2 of this work two reductive rank one $F$-groups, $/mathbf{H_1}$, $/mathbf{H_2}$, which are twisted endoscopic groups of $/textup{GSp}(2)$ with respect to a fixed quadratic character $/varepsilon$ of the idele class group of $F$ if $F$ is global, $F^/times$ if $F$ is local. When $F$ is global, Langlands functoriality predicts that there exists a canonical lifting of the automorphic representations of $/mathbf{H_1}$, $/mathbf{H_2}$ to those of $/textup{GSp}(2)$. In Chapter 4, the author establishes this lifting in terms of the Satake parameters which parameterize the automorphic representations. By means of this lifting he provides a classification of the discrete spectrum automorphic representations of $/textup{GSp}(2)$ which are invariant under tensor product with $/varepsilon$. Table of Contents: Introduction; $/varepsilon$-endoscopy for $/textup{GSp}(2)$; The trace formula; Global lifting; The local picture; Appendix A. Summary of global lifting; Appendix B. Fundamental lemma; Bibliography; List of symbols; Index. (MEMO/204/957)