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The Genuine Omega-regular Unitary Dual of the Metaplectic Group

  • Alessandra Pantano (a1), Annegret Paul (a2) and Susana A. Salamanca-Riba (a3)
Abstract

We classify all genuine unitary representations of the metaplectic group whose infinitesimal character is real and at least as regular as that of the oscillator representation. In a previous paper we exhibited a certain family of representations satisfying these conditions, obtained by cohomological induction from the tensor product of a one-dimensional representation and an oscillator representation. Our main theorem asserts that this family exhausts the genuine omega-regular unitary dual of the metaplectic group.

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References
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[1] Adams, J., Barbasch, D., Paul, A., Trapa, P., and Vogan, D., Unitary Shimura correspondences for split real groups. J. Amer. Math. Soc. 20(2007), no. 3, 701751. http://dx.doi.org/10.1090/S0894-0347-06-00530-3
[2] Huang, J.-S., The unitary dual of the universal covering group of GL(n, R). Duke Math. J. 61(1990), no. 3, 705745. http://dx.doi.org/10.1215/S0012-7094-90-06126-5
[3] Knapp, A. and Vogan, D., Cohomological induction and unitary representations. Princeton Mathematical Series, 45, Princeton University Press, Princeton, NJ, 1995.
[4] Pantano, A., Paul, A., and Salamanca-Riba, S., The omega-regular unitary dual of the metaplectic group of rank 2. In: Council for African American researchers in the mathematical sciences, V, Contemp. Math., 467, American Mathematical Society, Providence, RI, 2008, pp. 147.
[5] Pantano, A., Unitary genuine principal series of the metaplectic group. Represent. Theory 14(2010), 201248. http://dx.doi.org/10.1090/S1088-4165-10-00367-5
[6] Parthasaraty, R., Criteria for the uniterizability of some highest weight modules. Proc. Indian Acad. Sci. Sect. A Math. Sci. 89(1980), no. 1, 124. http://dx.doi.org/10.1007/BF02881021
[7] Paul, A., Howe correspondence for real unitary groups. J. Funct. Anal. 159(1998), no. 2, 384431. http://dx.doi.org/10.1006/jfan.1998.3330
[8] Paul, A., On the Howe correspondence for symplectic-orthogonal dual pairs. J. Funct. Anal. 228(2005), no. 2, 270310. http://dx.doi.org/10.1016/j.jfa.2005.03.015
[9] Salamanca-Riba, S., On the unitary dual of some classical Lie groups. Compositio Math. 68(1988), no. 3, 251303.
[10] Salamanca-Riba, S., On the unitary dual of real reductive Lie groups and the Aq(_)-modules: the strongly regular case. Duke Math. J. 96(1999), no. 3, 521546. http://dx.doi.org/10.1215/S0012-7094-99-09616-3
[11] Salamanca-Riba, S. and Vogan , D. A..Jr, On the classification of unitary representations of reductive Lie groups. Ann. of Math. 148(1998), no. 3, 10671133. http://dx.doi.org/10.2307/121036
[12] Vogan , D. A.Jr., Representations of real reductive lie groups. Progress in Mathematics, 15, Birkhäuser, Boston, MA, 1981.
[13] Vogan, D. A. Jr., Unitarizability of certain series of representations. Ann. of Math. 120(1984), no. 1, 141187. http://dx.doi.org/10.2307/2007074
[14] Vogan, D. A. Jr., The unitary dual of G2. Invent. Math. 116(1994), no. 1–3, 677791. http://dx.doi.org/10.1007/BF01231578
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Canadian Journal of Mathematics
  • ISSN: 0008-414X
  • EISSN: 1496-4279
  • URL: /core/journals/canadian-journal-of-mathematics
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