Dimension of the space of intertwining operators from degenerate principal series representations

• Taito Tauchi ^[1]
  1. [1] University of Tokyo

     University of Tokyo

     Japón

     
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 24, Nº. 4, 2018, págs. 3649-3662
• Idioma: inglés
• DOI: 10.1007/s00029-018-0422-2
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• Resumen

  • Let X be a homogeneous space of a real reductive Lie group G. It was proved by T. Kobayashi and T. Oshima that the regular representation C∞(X) contains each irreducible representation of G at most finitely many times if a minimal parabolic subgroup P of G has an open orbit in X, or equivalently, if the number of P-orbits on X is finite. In contrast to the minimal parabolic case, for a general parabolic subgroup Q of G, we find a new example that the regular representation C∞(X) contains degenerate principal series representations induced from Q with infinite multiplicity even when the number of Q-orbits on X is finite.