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

2017/08/02 by Taito Tauchi, Tauchi, Taito
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1708.00610

openalex publication_date 2017/08/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

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