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On symplectic periods and restriction to SL(2n)

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Abstract

We study representations of the general and the special linear groups over a non-archimedean local field that admit a non-zero invariant linear form with respect to the symplectic group (henceforth distinguished representations). For the class of ladder representations that are distinguished we show that applying the highest derivative operation twice results in a distinguished (ladder) representation. Furthermore, we characterize the unique distinguished component of the associated L-packet of representations of the special linear group in terms of the associated maximal unipotent orbit. We also obtain a sufficient condition for distinction of standard modules.

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Acknowledgements

I would like to thank Dipendra Prasad for conversations on his joint work with Sarah Dijols [6] that inspired this project. I also thank Dima Gourevitch for his patient clarifications concerning degenerate Whittaker models. Our conversations led us to deduce Lemma 5.4.

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  1. Department of Mathematics, Brandeis University, Waltham, MA, 02453, USA

    Omer Offen

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Offen, O. On symplectic periods and restriction to SL(2n). Math. Z. 294, 1521–1552 (2020). https://doi.org/10.1007/s00209-019-02390-x

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