On the Poincaré series of Kac-Moody Lie algebras

Jin chunhua; Zhao Xu-an

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arXiv · 1210.0648

On the Poincaré series of Kac-Moody Lie algebras

Jin chunhua·Zhao Xu-an

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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}.

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BibTeX RIS

Jin chunhua, Zhao Xu-an. 2012-10-02. On the Poincaré series of Kac-Moody Lie algebras. https://arxiv.org/abs/1210.0648

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