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The Genuine Omega-regular Unitary Dual of the Metaplectic Group
  Published:2011-10-22
 Printed: Jun 2012
Canadian Journal of Mathematics
  • Alessandra Pantano,
    Department of Mathematics, University of California at Irvine, Irvine, CA 92697, USA
  • Annegret Paul,
    Department of Mathematics, Western Michigan University, Kalamazoo, MI 49008, USA
  • Susana A. Salamanca-Riba,
    Department of Mathematics, New Mexico State University, Las Cruces, NM 88003, USA
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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.
Keywords: Metaplectic group, oscillator representation, bottom layer map, cohomological induction, Parthasarathy's Dirac Operator Inequality, pseudospherical principal series Metaplectic group, oscillator representation, bottom layer map, cohomological induction, Parthasarathy's Dirac Operator Inequality, pseudospherical principal series
MSC Classifications: 22E46 show english descriptions Semisimple Lie groups and their representations 22E46 - Semisimple Lie groups and their representations
 
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