ASSOCIATED SYMMETRIC PAIR AND MULTIPLICITIES OF ADMISSIBLE RESTRICTION OF DISCRETE SERIEs

VARGAS, JORGE A.

www.arXiv.org

Cornell University

Lugar: Ithaca; Año: 2013 p. 1 - 24

1976-5541

Let $( G,   H)$ be a symmetric  pair for a real semisimple Lie group $G$ and $(G, H_0)$   its associated pair. For each   irreducible square integrable representation $\pi$ of $G$ so that its restriction to $H$ is admissible, we find an irreducible square integrable representation $\pi_0$ of $H_0$ which allows to compute the Harish-Chandra parameter of each irreducible $H-$subrepresentation of $\pi$ as well as its multiplicity. The computation   is based on the spectral analysis of the restriction of  $\pi_0$ to a maximal compact subgroup of $H_0.$