Polynomial invariants of Weyl groups for Kac-Moody groups
Commutative Algebra
2016-01-20 v1 Algebraic Topology
Representation Theory
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 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.
Keywords
Cite
@article{arxiv.1211.3197,
title = {Polynomial invariants of Weyl groups for Kac-Moody groups},
author = {Zhao Xu-an and Jin Chunhua},
journal= {arXiv preprint arXiv:1211.3197},
year = {2016}
}
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16 pages