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Varna Lecture on L2-Analysis of Minimal Representations

  • Toshiyuki Kobayashi
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (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.

Keywords

Jordan Algebra Minimal Representation Irreducible Unitary Representation Geometric Quantization Nilpotent Orbit 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

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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Copyright information

© Springer Japan 2013

Authors and Affiliations

  1. 1.Kavli IPMU and Graduate School of Mathematical SciencesThe University of TokyoTokyoJapan

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