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Degenerate principal series representations forU(n, n)

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Abstract

For a quadratic extensionE/F of a nonarchimedean local field of characteristic other than 2, letG=U (n, n) be the quasisplit unitary group of rankn, and letP be the maximal parabolic subgroup ofG which stabilizes a maximal isotropic subspace. ThenP has a Levi decompositionP=MN withM ≃ GL (n, E). In this paper, the points of reducibility and composition series of the degenerate principal seriesI n (s, χ) defined by characters ofM are determined completely. The constituents arising as theta lifts of characters ofU (m)'s are identified and their behavior under the intertwining operator\(M(s,\chi ):I_n (s,\chi ) \to I_n (s,\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{\chi } )\)) is described. The caseE=F⊕F andG≃GL (2n, F) is included.

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Authors and Affiliations

  1. Department of Mathematics, University of Maryland, 20742-0001, College Park, MD, USA

    Stephen S. Kudla

  2. Florida International University, University Park, 33199-0001, Miami, FL, USA

    W. Jay Sweet

Authors
  1. Stephen S. Kudla
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  2. W. Jay Sweet
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Correspondence to Stephen S. Kudla.

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Partially supported by NSF Grant number DMS-9302539.

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Kudla, S.S., Jay Sweet, W. Degenerate principal series representations forU(n, n) . Israel J. Math. 98, 253–306 (1997). https://doi.org/10.1007/BF02937337

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  • DOI: https://doi.org/10.1007/BF02937337

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