University of Arizona
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Title: L-functions for Sp(2n)xGL(k) via non-unique models
Abstract: In the usual paradigm of the Rankin-Selberg method, the Eulerian factorization of a global integral relies on the uniqueness of a model such as the Whittaker model, or the uniqueness of an invariant bilinear form between an irreducible representation and its contragredient. Examples of Rankin-Selberg integrals which unfold to non-unique models are very rare because standard tools for local unramified computation such as the Casselman-Shalika formula are not applicable. In this talk we derive new global integrals for Sp(2n)xGL(k) where n is even, from the generalized doubling method of Cai, Friedberg, Ginzburg and Kaplan, following a strategy and extending a previous result of Ginzburg and Soudry on the case n=k=2. We show that these new global integrals unfold to non-unique models on Sp(2n). Using the New Way method of Piatetski-Shapiro and Rallis, we show that these new global integrals represent the L-functions for Sp(2n)xGL(k), generalizing a previous work of Piatetski-Shapiro and Rallis on Sp(2n)xGL(1). This is joint work with Yubo Jin.