branching laws, examples and some new results

MARQUEZ, SIMONDI, VARGAS

arXiv.org

Cornell university

Lugar: Cornell; Año: 2018 p. 1 - 15

For a connected, noncompact matrix simple Lie group G so that a maximalcompact subgroup K has three dimensional simple ideal, in this note weanalyze the admissibility of the restriction of irreducible square integrablerepresentations for the ambient group when they are restricted to certainsubgroups that contains the three dimensional ideal. In this setting we providea formula for the multiplicity of the irreducible factors. Also, for generalG such that G/K is an Hermitian G-manifold we give a necessary andsufficient condition so that a square integrable representations of the ambientgroup is admissible over the semisimple factor of K.