IWASAWA DECOMPOSITION OF AFFINE KAC-MOODY ALGEBRAS USING SATAKE DIAGRAMS

We carry out the Iwasawa decomposition of the affine Kac-Moody algebra s within the general framework of involutive automorphisms which are d etermined with the help of the Satake diagrams corresponding to these algebras. The parabolic subalgebras essential for the construction of induced representations are computed from the Langlands decomposition. In particular, we consider the untwisted versions, viz., A(1)((1)) an d A(2)((1)), as representative examples for the purpose of illustratio n. (C) 1998 American Institute of Physics.