Pseudo-dual pairs and branching of Discrete Series

Autor: Ørsted, Bent, Vargas, Jorge A.
Rok vydání: 2023
Předmět:
Druh dokumentu: Working Paper
Popis: 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.
Comment: To appear in "Symmetry in Geometry and Analysis -- Festschrift for Toshiyuki Kobayashi''. M. Pevzner und H. Sekiguchi eds., Progress in Mathematics, Springer 2024
Databáze: arXiv
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