Abstract
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.
Original language | English |
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Journal | Duke Mathematical Journal |
Volume | 169 |
Issue | 18 |
Pages (from-to) | 3477-3537 |
Number of pages | 61 |
ISSN | 0012-7094 |
DOIs | |
Publication status | Published - 2020 |