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

Taito Tauchi

• 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.