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Local Rankin–Selberg integrals for Speh representations

  • Erez M. Lapid (a1) and Zhengyu Mao (a2)

Abstract

We construct analogues of Rankin–Selberg integrals for Speh representations of the general linear group over a $p$ -adic field. The integrals are in terms of the (extended) Shalika model and are expected to be the local counterparts of (suitably regularized) global integrals involving square-integrable automorphic forms and Eisenstein series on the general linear group over a global field. We relate the local integrals to the classical ones studied by Jacquet, Piatetski-Shapiro and Shalika. We also introduce a unitary structure for Speh representation on the Shalika model, as well as various other models including Zelevinsky’s degenerate Whittaker model.

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This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.

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The second named author is partially supported by NSF grant DMS 1700637.

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References

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Local Rankin–Selberg integrals for Speh representations

  • Erez M. Lapid (a1) and Zhengyu Mao (a2)

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