Asian Journal of Mathematics
- Asian J. Math.
- Volume 18, Number 5 (2014), 885-928.
Tame Fréchet structures for affine Kac-Moody groups
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.
Asian J. Math., Volume 18, Number 5 (2014), 885-928.
First available in Project Euclid: 2 December 2014
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Freyn, Walter. Tame Fréchet structures for affine Kac-Moody groups. Asian J. Math. 18 (2014), no. 5, 885--928. https://projecteuclid.org/euclid.ajm/1417489246