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Varna Lecture on L 2-Analysis of Minimal Representations

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Lie Theory and Its Applications in Physics

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 36))

Abstract

Minimal representations of a real reductive group G are the ‘smallest’ irreducible unitary representations of G. The author suggests a program of global analysis built on minimal representations from the philosophy:

small representation of a group = large symmetries in a representation space.

This viewpoint serves as a driving force to interact algebraic representation theory with geometric analysis of minimal representations, yielding a rapid progress on the program. We give a brief guidance to recent works with emphasis on the Schrödinger model.

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Acknowledgements

The author warmly thanks Professor Vladimir Dobrev for his hospitality during the ninth International Workshop: Lie Theory and its Applications in Physics in Varna, Bulgaria, 20–26 June 2011. Thanks are also due to anonymous referees for careful readings.

The author was partially supported by Grant-in-Aid for Scientific Research (B) (22340026), Japan Society for the Promotion of Sciences.

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Authors and Affiliations

  1. Kavli IPMU and Graduate School of Mathematical Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro, 153-8914, Tokyo, Japan

    Toshiyuki Kobayashi

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  1. Toshiyuki Kobayashi
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Correspondence to Toshiyuki Kobayashi .

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  1. Bulgarian Academy of Sciences, 72 Tsarigradsko Chaussee, Sofia, 1784, Sofiya, Bulgaria

    Vladimir Dobrev

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Kobayashi, T. (2013). Varna Lecture on L 2-Analysis of Minimal Representations. In: Dobrev, V. (eds) Lie Theory and Its Applications in Physics. Springer Proceedings in Mathematics & Statistics, vol 36. Springer, Tokyo. https://doi.org/10.1007/978-4-431-54270-4_6

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