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Isomorphisms of Kac-Moody groups

✍ Scribed by Pierre-Emmanuel Caprace; Bernhard Mühlherr

Publisher
Springer-Verlag
Year
2005
Tongue
English
Weight
762 KB
Volume
161
Category
Article
ISSN
0020-9910

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In this paper we prove a lemma about the Weyl groups of Kac᎐Moody algebras and decompose the Weyl group of some Kac᎐Moody algebras into a semi-direct product of two subgroups which are Coxeter groups.

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We give a complete and explicit description for all two-dimensional representations of non-twisted affine Kac-Moody groups. Those representations are found having a unique form characterized by homomorphisms between the base fields. The homomorphisms from affine Kac-Moody groups to two-dimensional l