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Distinguished tame supercuspidal representations of symmetric pairs (Sp4n (F), Sp2n (E))

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Let (G, H) be a symmetric pair defined over a p-adic field F and π be an irreducible tame supercuspidal representation of G, defined by Yu (J Am Math Soc 3:579–622, 2001). Hakim and Murnaghan (Int Math Res Pap IMRP 166(2): Art. ID rpn005 2008) give a dimension formula for the space \({{\rm Hom}_{H}(\pi, {1\!\!1})}\) in terms of generic cuspidal data. In this paper, we consider the symmetric pair (Sp4n (F), Sp2n (E)) where E is a quadratic extension over F, and give sufficient and necessary conditions on such generic cuspidal data whose corresponding tame supercuspidal representations are H-distinguished. In addition, for the symmetric pair (U2n (J, F), Sp2n (F)) there is no Sp2n (F)-distinguished tame supercuspidal representation of U2n (J, F).

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Correspondence to Lei Zhang.

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Appendix by Dihua Jiang and Lei Zhang.

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Zhang, L. Distinguished tame supercuspidal representations of symmetric pairs (Sp4n (F), Sp2n (E)). manuscripta math. 148, 213–233 (2015). https://doi.org/10.1007/s00229-015-0742-x

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