info:eu-repo/semantics/article
Branching problems in reproducing kernel spaces
Fecha
2020-12-01Registro en:
Ørsted, Bent; Vargas, Jorge Antonio; Branching problems in reproducing kernel spaces; Duke University Press; Duke Mathematical Journal; 169; 18; 1-12-2020; 3477-3537
0012-7094
CONICET Digital
CONICET
Autor
Ørsted, Bent
Vargas, Jorge Antonio
Resumen
For a semisimple Lie group G satisfying the equal-rank condition, the most basic family of unitary irreducible representations is the discrete series found by Harish-Chandra. In our work here we study some of the branching laws for discrete series when restricted to a subgroup H of the same type by combining classical results with recent work of Kobayashi; in particular, we prove discrete decomposability under Harish-Chandra’s condition of cusp form on the reproducing kernel. We show a relation between discrete decomposability and representing certain intertwining operators in terms of differential operators.