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Generalized semi-invariant distributions on p-adic spaces

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Abstract

In this paper we investigate some methods on calculating the spaces of generalized semi-invariant distributions on p-adic spaces. Using homological methods, we give a criterion of automatic extension of (generalized) semi-invariant distributions. Based on the meromorphic continuations of Igusa zeta integrals, we give another criteria with purely algebraic geometric conditions, on the extension of generalized semi-invariant distributions.

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Acknowledgments

J. Hong would like to thank Rami Aizenbud, Joseph Bernstein and Yiannis Sakellaridis for helpful discussions. He also would like to thank AMSS, Chinese Academy of Science for the hospitality during his two visits in July–August and December of 2013, where part of the work was done. B. Sun was supported by the NSFC Grants 11525105, 11321101, and 11531008. Finally, both authors would like to thank the anonymous referee for many valuable comments which have led to an improvement of this paper.

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Authors and Affiliations

  1. Department of Mathematics, University of North Carolina at Chapel Hill, CB 3250 Phillips Hall, Chapel Hill, NC, 27599-3250, USA

    Jiuzu Hong

  2. Hua Loo-Keng Key Laboratory of Mathematics, Institute of Mathematics, AMSS, Chinese Academy of Sciences, Beijing, 100190, People’s Republic of China

    Binyong Sun

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  1. Jiuzu Hong
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  2. Binyong Sun
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Correspondence to Jiuzu Hong.

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Communicated by A. Venkatesh.

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Hong, J., Sun, B. Generalized semi-invariant distributions on p-adic spaces. Math. Ann. 367, 1727–1776 (2017). https://doi.org/10.1007/s00208-016-1444-8

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  • DOI: https://doi.org/10.1007/s00208-016-1444-8

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