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Global Differential Geometry pp 55–92Cite as

Kac-Moody Geometry

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Part of the book series: Springer Proceedings in Mathematics ((PROM,volume 17))

Abstract

The geometry of symmetric spaces, polar actions, isoparametric submanifolds and spherical buildings is governed by spherical Weyl groups and simple Lie groups. The most natural generalization of semisimple Lie groups are affine Kac-Moody groups as they mirror their structure theory and have good explicitly known representations as groups of operators. In this article we describe the infinite dimensional differential geometry associated to affine Kac-Moody groups: Kac-Moody symmetric spaces, isoparametric submanifolds in Hilbert space, polar actions on Hilbert spaces and universal geometric twin buildings.

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Authors and Affiliations

  1. Institut für Mathematik, Universität Münster, Einsteinstrasse 62, 48149, Münster, Germany

    Walter Freyn

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  1. Walter Freyn
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Correspondence to Walter Freyn .

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Editors and Affiliations

  1. Inst. Mathematik, Universität Potsdam, Potsdam, Brandenburg, Germany

    Christian Bär

  2. , Mathematisches Institut, Universität Münster, Einsteinstraße 62, Münster, 48149, Germany

    Joachim Lohkamp

  3. , Fakultät für Mathematik und Informatik, Universität Leipzig, Johannisgasse 26, Leipzig, 04103, Sachsen, Germany

    Matthias Schwarz

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Freyn, W. (2012). Kac-Moody Geometry. In: Bär, C., Lohkamp, J., Schwarz, M. (eds) Global Differential Geometry. Springer Proceedings in Mathematics, vol 17. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22842-1_3

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