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

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Book cover Representation Theory and Automorphic Forms

Part of the book series: Progress in Mathematics ((PM,volume 255))

Summary

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.

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  1. RIMS, Kyoto University, Kyoto 606-8502, Japan

    Toshiyuki Kobayashi

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  1. Toshiyuki Kobayashi
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Editors and Affiliations

  1. RIMS, Kyoto University, Sakyo-ku, Kyoto, 606-8502, Japan

    Toshiyuki Kobayashi

  2. Department of Mathematics, Harvard University, Cambridge, MA 02138, U.S.A

    Wilfried Schmid

  3. Department of Mathematics, Inha University, Incheon 402-751, Republic of Korea

    Jae-Hyun Yang

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Kobayashi, T. (2008). Multiplicity-free Theorems of the Restrictions of Unitary Highest Weight Modules with respect to Reductive Symmetric Pairs. In: Kobayashi, T., Schmid, W., Yang, JH. (eds) Representation Theory and Automorphic Forms. Progress in Mathematics, vol 255. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-4646-2_3

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