On the Poincaré series of Kac-Moody Lie algebras

Abstract

In this paper, we discuss the Poincaré series of Kac-Moody Lie algebras, especially for indefinite type. Firstly, we compute the Poincaré series of certain indefinite Kac-Moody Lie algebras whose Cartan matrices have the same type of $2\times 2$ principal sub-matrices. Secondly, we show that the Poincaré series of Kac-Moody Lie algebras satisfy certain interesting properties. Lastly we give some applications of the Poincaré series to other fields. Particularly we construct some counter examples to a conjecture of Victor Kac\cite{Kac_85} and a conjecture of Chapavalov, Leites and Stekolshchik\cite{CDR_10}.

15 pages

Cited by in corpus (2)

• Poincaré series and rational cohomology rings of Kac-Moody groups and their flag manifolds
• The ranks of homotopy groups of Kac-Moody groups