Polynomial invariants of Weyl groups for Kac–Moody groups

Zhao Xu-an and Jin Chunhua

Vol. 269 (2014), No. 2, 491–509

DOI: 10.2140/pjm.2014.269.491

Abstract

We prove that the ring of polynomial invariants of Weyl group for an indecomposable and indefinite Kac–Moody Lie algebra is generated by the invariant symmetric bilinear form or is trivial depending on whether $A$ is symmetrizable or not. The result was conjectured by Moody and assumed by Kac. As an application, we discuss the rational homotopy types of Kac–Moody groups and their flag manifolds.

Keywords

Cartan matrix, Weyl group, polynomial invariants of Weyl group, Kac–Moody Group, flag manifold, cohomology of Kac–Moody groups

Mathematical Subject Classification 2010

Primary: 17C99

Secondary: 55N45

Milestones

Received: 12 March 2013

Revised: 17 November 2013

Accepted: 30 December 2013

Published: 26 July 2014