Associated symmetric pair and multiplicities of admissible restriction of Discrete Series.

VARGAS, JORGE A.

Pucon, Chile

Congreso; XIX coloquio latinoamericano de algebra; 2012

SOMACHI

Let (G;H) be a symmetric pair for a real semisimple Lie group G and (G;H0) theassociated pair. For each irreducible square integrable representation  of G so that itsrestriction to H is admissible, we find an irreducible square integrable representation0 of H0 which allows to compute the Harish-Chandra parameter of each irreducibleH􀀀subrepresentation of  as well as its multiplicity. The computation is based on thespectral analysis of the restriction of 0 to a maximal compact subgroup of H0 and aconvenient branching law for the the lowest K􀀀type of :