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A FUNDAMENTAL LEMMA BETWEEN THE SYMPLECTIC AND THE METAPLECTIC GROUP: THE NON-SPLIT CASE
Keywords:
fundamental lemma, relative trace formula, descent, symplectic group, metaplectic groupAbstract
Let $F$ be a number field with ring of adeles $A$, and let $K / F$ be a quadratic extension. We prove the fundamental lemma for a relative trace identity between $S p_{2 n}(A)$ and $\widetilde{S p_n}(A)$. This completes proof of a relative trace formula between $G L_{2 n}(A)$ and $\widetilde{S p_n}(A)$. As consequences, we expect a generalization of work of Kohnen [4] and a verification of a conjecture of Furusawa and Martin [2] characterizing $G L_n(K)$-distinction of cuspidal representations of $G L_{2 n}(A)$.
Received: December 2, 2022
Accepted: December 26, 2022
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