On the metaplectic analog of Kazhdan's ``endoscopic'' lifting
Let k'/k be a cyclic extension of degree r of number fields. Suppose that x \(n=1\) has n solutions in k. Let D be a division algebra of dimension r 2 over k. We let T (resp. \(G_ D)\) be the algebraic group so that for any k-algebra A one has \(T(A)=(A\otimes_ kk')^{\times}\) (resp. \(G_ D(A)=(A\otimes_ kD)^{\times})\). The endoscopic lifting of the title is a lifting of automorphic representations of \(T(k_ A)\) (i.e. Größencharaktere of k') to automorphic representations of \(GL_ r(k_ A)\). Let \(\tilde T\) (resp. \(\tilde G_ D)\) be suitable n-fold metaplectic covers of \(T(k_ A)\) (resp. \(G_ D(k_ A))\). Then under the assumption that k' splits D and various other technical assumptions the author proves a correspondence between automorphic representations of \(\tilde T\) and a well defined subset of those of \(\tilde G_ D\). This is done using a simple version of the Selberg trace formula.
scientific article; zbMATH DE number 4049906
scientific article