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November 2014 Tame Fréchet structures for affine Kac-Moody groups
Walter Freyn
Asian J. Math. 18(5): 885-928 (November 2014).

Abstract

We construct holomorphic loop groups and their associated affine Kac-Moody groups and prove that they are tame Fréchet manifolds; furthermore we study the adjoint action of these groups. These results form the functional analytic core for a theory of affine Kac-Moody symmetric spaces, that will be developed in forthcoming papers. Our construction also solves the problem of complexification of completed Kac-Moody groups: we obtain a description of complex completed Kac-Moody groups and, using this description, deduce constructions of their non-compact real forms.

Citation

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Walter Freyn. "Tame Fréchet structures for affine Kac-Moody groups." Asian J. Math. 18 (5) 885 - 928, November 2014.

Information

Published: November 2014
First available in Project Euclid: 2 December 2014

zbMATH: 1311.22029
MathSciNet: MR3287007

Subjects:
Primary: 20G44, 22E67

Rights: Copyright © 2014 International Press of Boston

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Vol.18 • No. 5 • November 2014
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