Pseudo-dual pairs and branching of Discrete Series

Autor:	Ørsted, Bent, Vargas, Jorge A.
Rok vydání:	2023
Předmět:	Mathematics - Representation Theory Mathematics - Functional Analysis Primary 22E46 Secondary 17B10
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
Externí odkaz:	http://arxiv.org/abs/2302.14190 Zobrazit plný text záznamu View this record from Arxiv