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On branching laws of Speh representations

Ito, Nozomi 京都大学 DOI:10.14989/doctor.k23674

2022.03.23

概要

In this paper, we consider the branching law of the Speh representation Sp(π, n + l) of GL2n+2l with respect to the block diagonal subgroup GLn GLn+2l for any generic representation π of GL2 over any p-adic field. We use the Shalika model of Sp(π, n) to construct certain zeta integrals, which were constructed by Ginzburg and Kaplan independently, and study them. Finally, using these zeta integrals, we obtain a nonzero GLn GLn+2l-map from Sp(π, n + l) to τ ⊠ τ ∨χπ Sp(π, l) for any irreducible representation τ of GLn. These results form part of the local theory of the Miyawaki lifting for unitary groups.

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