Pseudo-dual pairs and branching of Discrete Series

2023/02/27 by Bent Ørsted, Ørsted, Bent, Jorge A. Vargas +1
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Functional Analysis (math.FA) #Primary 22E46 #Representation Theory (math.RT) #Secondary 17B10

paper · pdf · doi:10.48550/arxiv.2302.14190

openalex publication_date 2023/02/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For a semisimple Lie group G, we study Discrete Series representations with admissible branching to a symmetric subgroup H. This is done using a canonical associated symmetric subgroup H₀, forming a pseudo-dual pair with H, and a corresponding branching law for this group with respect to its maximal compact subgroup. This is in analogy with either Blattner's or Kostant-Heckmann multiplicity formulas, and has some resemblance to Frobenius reciprocity. We give several explicit examples and links to Kobayashi-Pevzner theory of symmetry breaking and holographic operators. Our method is well adapted to computer algorithms, such as for example the Atlas program.

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