On the Unitarization of Highest Weight Representations for Affine Kac-moody Algebras
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چکیده
In a recent paper ([1],[2]) we have classified explicitely all the unitary highest weight representations of non compact real forms of semisimple Lie Algebras on Hermitian symmetric space. These results are necessary in order to construct all the unitary highest weight representations of affine Kac-Moody Algebras following some theorems proved by Jakobsen and Kac ([3],[4]). 1. The Affine Kac-Moody Algebra Let ġ be a finite dimensional semisimple complex Lie algebra with Chevalley basis {Hα, Eα, Fα} with α belonging to the set of simple roots. The elements of the so-called Cartan matrix A are defined by Ajk = αk (Hαj) = 2 (αk, αj) (αj, αj) , j, k = 1, 2, . . . , l where, (αj, αk) = B (
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تاریخ انتشار 2003