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Polynomial invariants of Weyl groups for Kac-Moody groups (1211.3197v1)
Published 14 Nov 2012 in math.AC, math.AT, and math.RT
Abstract: In this paper, we prove that the ring of polynomial invariants of the Weyl group for an indecomposable and indefinite Kac-Moody Lie algebra is generated by invariant symmetric bilinear form or is trivial depending on $A$ is symmetrizable or not. The result was conjectured by Moody and assumed by Kac. As applications we discuss the rational homotopy types of Kac-Moody groups and their flag manifolds.
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