Local Rankin–Selberg integrals for Speh representations
2020 ◽
Vol 156
(5)
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pp. 908-945
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Keyword(s):
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.
1982 ◽
Vol 12
(1)
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pp. 123-144
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2010 ◽
Vol 62
(6)
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pp. 1340-1386
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Keyword(s):
1988 ◽
Vol 43
(4)
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pp. 2533-2540
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2004 ◽
Vol 282
(1)
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pp. 368-385
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Keyword(s):
1979 ◽
Vol 28
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pp. 53-62
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2015 ◽
Vol 469
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pp. 169-203
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