ASSOCIATED SYMMETRIC PAIR AND MULTIPLICITIES OF ADMISSIBLE RESTRICTION OF DISCRETE SERIEs

VARGAS, JORGE A.

INTERNATIONAL JOURNAL OF MATHEMATICS

WORLD SCIENTIFIC PUBL CO PTE LTD

Lugar: London, UK; Año: 2016 p. 1 - 29

0129-167X

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 $H_0.$