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A general form of Gelfand–Kazhdan criterion

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Abstract

We formalize the notion of matrix coefficients for distributional vectors in a representation of a real reductive group, which consist of generalized functions on the group. As an application, we state and prove a Gelfand–Kazhdan criterion for a real reductive group in very general settings.

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Authors and Affiliations

  1. Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, People’s Republic of China

    Binyong Sun

  2. Department of Mathematics, National University of Singapore, Block S17, 10 Lower Kent Ridge Road, Singapore, 119076, Singapore

    Chen-Bo Zhu

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  1. Binyong Sun
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  2. Chen-Bo Zhu
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Correspondence to Chen-Bo Zhu.

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Sun, B., Zhu, CB. A general form of Gelfand–Kazhdan criterion. manuscripta math. 136, 185–197 (2011). https://doi.org/10.1007/s00229-011-0437-x

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  • DOI: https://doi.org/10.1007/s00229-011-0437-x

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