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Howe duality and dichotomy for exceptional theta correspondences

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Abstract

We study three exceptional theta correspondences for p-adic groups, where one member of the dual pair is the exceptional group \(G_2\). We prove the Howe duality conjecture for these dual pairs and a dichotomy theorem, and determine explicitly the theta lifts of all non-cuspidal representations.

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Acknowledgements

The authors would like to thank MFI in Oberwolfach for hospitality during a conference in October of 2019 when some of the ideas needed to finish this work emerged. Thanks are due to Petar Bakić, Baiying Liu and Yiannis Sakellaridis for help with some finer points. W.T. Gan is partially supported by an MOE Tier 1 Grant R-146-000-320-114. G. Savin is partially supported by a National Science Foundation Grant DMS-1901745.

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Authors and Affiliations

  1. Department of Mathematics, National University of Singapore, 10 Lower Kent Ridge Road, Singapore, 119076, Singapore

    Wee Teck Gan

  2. Department of Mathematics, University of Utah, Salt Lake City, UT, USA

    Gordan Savin

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  1. Wee Teck Gan
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Gan, W.T., Savin, G. Howe duality and dichotomy for exceptional theta correspondences. Invent. math. 232, 1–78 (2023). https://doi.org/10.1007/s00222-022-01165-2

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