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2 results

  • The Genuine Omega-regular Unitary Dual of the Metaplectic Group

  • Alessandra Pantano, Annegret Paul, Susana A. Salamanca-Riba
  • Journal:
    Canadian Journal of Mathematics / Volume 64 / Issue 3 / 01 June 2012
    Published online by Cambridge University Press:
    20 November 2018, pp. 669-704
    Print publication:
    01 June 2012
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  • 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.

  • Matrix coefficients of cohomologically induced representations

  • Binyong Sun
  • Journal:
    Compositio Mathematica / Volume 143 / Issue 1 / January 2007
    Published online by Cambridge University Press:
    19 January 2007, pp. 201-221
    Print publication:
    January 2007
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  • We define integral formulas which produce certain matrix coefficients of cohomologically induced representations of real reductive groups. They are analogous to Harish-Chandra's Eisenstein integrals for matrix coefficients of ordinary induced representations, and generalize Flensted-Jensen's fundamental functions for discrete series.