Pseudo-dual pairs and branching of Discrete Series
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866913231548710912 |
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| author | Ørsted, Bent Vargas, Jorge A. |
| author_facet | Ørsted, Bent Vargas, Jorge A. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_14190 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Pseudo-dual pairs and branching of Discrete Series Ørsted, Bent Vargas, Jorge A. Representation Theory Functional Analysis Primary 22E46, Secondary 17B10 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. |
| title | Pseudo-dual pairs and branching of Discrete Series |
| topic | Representation Theory Functional Analysis Primary 22E46, Secondary 17B10 |
| url | https://arxiv.org/abs/2302.14190 |