Abstract
Let F be a local non-Archimedean field of characteristic zero with a finite residue field. Based on Tadić’s classification of the unitary dual of \({\mathrm {GL}}_{2n}(F)\), we classify irreducible unitary representations of \({\mathrm {GL}}_{2n}(F)\) that have nonzero linear periods, in terms of Speh representations that have nonzero periods. We also give a necessary and sufficient condition for the existence of a nonzero linear period for a Speh representation.
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Acknowledgements
The author thanks Wee Teck Gan for his kindness of sharing his paper [8] with us. He would also like to thank Dipendra Prasad for helpful comments and suggestions to improve the paper. The author thanks the referee for many remarks and suggestions and for pointing out an error in an earlier draft of the paper. The author was supported by the National Natural Science Foundation of China (no.12001191).
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This work was supported in part by the National Natural Science Foundation of China (no. 12001191).
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Yang, C. Linear periods for unitary representations. Math. Z. 302, 2253–2284 (2022). https://doi.org/10.1007/s00209-022-03136-y
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DOI: https://doi.org/10.1007/s00209-022-03136-y