A relative trace formula between the general linear and the metaplectic group. (English) Zbl 1307.11064
Summary: Let \(F\) be a number field with ring of adeles \(\mathbb{A}\) and let \(K/F\) be a quadratic extension. We prove part of a relative trace identity between \(\mathrm{GL}_{2n}(\mathbb{A})\) and the metaplectic group \(\widetilde{\mathrm{Sp}_n}(\mathbb{A})\). As consequences, we expect a generalization of work of W. Kohnen [Math. Ann. 271, 237–268 (1985; Zbl 0542.10018)] and a verification of a conjecture of M. Furusawa and K. Martin [J. Number Theory 146, 150–170 (2015; Zbl 1366.11076)] characterizing \(\mathrm{GL}_{n}(K)\)-distinction of a cuspidal representation of \(\mathrm{GL}_{2n}(\mathbb{A})\).
MSC:
11F72 | Spectral theory; trace formulas (e.g., that of Selberg) |
11F70 | Representation-theoretic methods; automorphic representations over local and global fields |