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A Formal Chevalley Restriction Theorem for Kac–Moody Groups

Published online by Cambridge University Press:  04 December 2007

Claus Mokler
Claus Mokler
Affiliation:
Fachbereich Mathematik, Universität Wuppertal, Gauβstraβe 20, D-42097 Wuppertal, Germany. e-mail: [email protected]
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Abstract

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Let G be a symmetrizable Kac–Moody group over a field of characteristic zero, let T be a split maximal torus of G. By using a completion of the algebra of strongly regular functions on G, and its restriction on T, we give a formal Chevalley restriction theorem. Specializing to the affine case, and to the field of complex numbers, we obtain a convergent Chevalley restriction theorem, by choosing the formal functions, which are convergent on the semi-groups of trace class elements Gtr⊂G resp. Ttr⊂T.

Keywords

Chevalley restriction theoreminvariant theory of exponential typeKac–Moody groups
Type
Research Article
Information
Compositio Mathematica , Volume 135 , Issue 2 , January 2003 , pp. 123 - 152
Copyright
© 2003 Kluwer Academic Publishers