Poincaré series and rational cohomology rings of Kac-Moody groups and their flag manifolds

Abstract

In this paper, we study the rational cohomology rings of indefinite Kac-Moody groups and their flag manifolds. By extracting the information of cohomology from the Poincaré series, we are able to determine the rational cohomology rings of Kac-Moody groups and their flag manifolds. Since Kac-Moody groups and their flag manifolds are rational formal, we also determine their rational homotopy groups and rational homotopy types.

10 pages

References in corpus (1)

• On the Poincaré series of Kac-Moody Lie algebras

Cited by in corpus (1)

• The ranks of homotopy groups of Kac-Moody groups