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The multiplicity problems for the unitary Ginzburg-Rallis models

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Abstract

We consider the local multiplicity problems for the analog of the Ginzburg—Rallis model for unitary groups and unitary similitude groups. For the unitary similitude group case, by proving a local trace formula for the model, we prove a multiplicity formula for all tempered representations, which implies that the summation of the multiplicities is equal to 1 over every tempered local Vogan L-packet. For the unitary group case, we also prove a multiplicity formula for all tempered representations which implies that the summation of the multiplicities is equal to 2 over every tempered local Vogan L-packet.

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Authors and Affiliations

  1. Department of Mathematics & Computer Science, Rutgers University - Newark, Newark, NJ, 07102, USA

    Chen Wan

  2. Department of Mathematics, National University of Singapore, Singapore, Singapore

    Lei Zhang

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  1. Chen Wan
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  2. Lei Zhang
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Correspondence to Chen Wan.

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Wan, C., Zhang, L. The multiplicity problems for the unitary Ginzburg-Rallis models. Isr. J. Math. 258, 185–248 (2023). https://doi.org/10.1007/s11856-023-2471-2

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  • DOI: https://doi.org/10.1007/s11856-023-2471-2

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