Multiplicity-free Theorems of the Restrictions of Unitary Highest Weight Modules with respect to Reductive Symmetric Pairs

By Toshiyuki Kobayashi. 2006

113 citations recorded by the source corpus.

The complex analytic methods have found a wide range of applications in the study of multiplicity-free representations. This article discusses, in particular, its applications to the question of restricting highest weight modules with respect to reductive symmetric pairs. We present a number of multiplicity-free branching theorems that include the multiplicity-free property of some of known results such as the Clebsh–Gordan–Pieri formula for tensor products, the Plancherel theorem for Hermitian symmetric spaces (also for line bundle cases), the Hua–Kostant–Schmid K-type formula, and the canonical representations in the sense of Vershik–Gelfand–Graev. Our method works in a uniform manner for both finite and infinite dimensional cases, for both discrete and continuous spectra, and for both classical and exceptional cases.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/3d10c9fc99de3f7b17633825d3468dd83fc087df

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In Algebra and Number Theory

1. M. Pevzner
2. Toshiyuki Kobayashi

In Geometry and Topology

1. M. Pevzner
2. Toshiyuki Kobayashi

In Mathematical Physics

1. M. Pevzner
2. Toshiyuki Kobayashi

Citations in the corpus

• Differential symmetry breaking operators: II. Rankin–Cohen operators for symmetric pairs (2015, methodology): “generally, the branching laws for holomorphic discrete series representations of scalar type in the setting of reductive symmetric pairs remain multiplicity-free for positive parameters [24], aswell as their counterpart for generalizedVermamodules for generic parameters [25].”
• Differential symmetry breaking operators: I. General theory and F-method (2015, background): “6) are equal to one (see [9]) and it becomesmeaningful to describe the projector from HG V to each G ′-irreducible summand.”