A relative trace formula between the general linear and the metaplectic group. II: Descent. (English) Zbl 1499.11209
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 formula between \(\mathrm{GL}_{2n}(\mathbb A)\) and \(\widetilde{\mathrm{Sp}}_n(\mathbb A)\) corresponding to the descent between \(\mathrm{Sp}_{2n}(\mathbb A)\) and \(\widetilde{\mathrm{Sp}}_n(\mathbb A)\). As consequences, we expect a generalization of work of Kohnen and a verification of a conjecture of Furusawa and Martin characterizing \(\mathrm{GL}_n(K)\)-distinction of cuspidal representations of \(\mathrm{GL}_{2n}(\mathbb A)\).
For Part I, see [ibid. 34, No. 2, 83–107 (2014; Zbl 1307.11064)].
For Part I, see [ibid. 34, No. 2, 83–107 (2014; Zbl 1307.11064)].
MSC:
| 11F72 | Spectral theory; trace formulas (e.g., that of Selberg) |
| 11F70 | Representation-theoretic methods; automorphic representations over local and global fields |
Citations:
Zbl 1307.11064References:
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