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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-Heckman 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 the Atlas program.

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Pseudo-dual Pairs and Branching of Discrete Series

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  • 发表日期：

    2025年

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  • Bent Ørsted,
  • Jorge A. Vargas

摘要

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-Heckman 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 the Atlas program.