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arXiv · 2302.14190

Pseudo-dual pairs and branching of Discrete Series

Bent Ørsted·Jorge A. Vargas
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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 $H_0$, 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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Bent Ørsted, Jorge A. Vargas. 2023-02-27. Pseudo-dual pairs and branching of Discrete Series. https://arxiv.org/abs/2302.14190

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