Pseudo-dual pairs and branching of Discrete Series

VARGAS JORGE

arXiv.org

Cornell University

Lugar: Cornell; Año: 2023 p. 1 - 53

2331-8422

For a semisimple Lie group G, we study Discrete Seriesrepresentations with admissible branching to a symmetric subgroupH. This is done using a canonical associated symmetricsubgroup H0, forming a pseudo-dual pair with H, and a correspondingbranching law for this group with respect to its maximalcompact subgroup. This is in analogy with either Blattner’sor Kostant-Heckmann multiplicity formulas, and has some resemblanceto Frobenius reciprocity. We give several explicit examplesand links to Kobayashi-Pevzner theory of symmetry breaking andholographic operators. Our method is well adapted to computeralgorithms, such as for example the Atlas program