On the Poincaré series of Kac-Moody Lie algebras

2012/10/02 by chunhua, Jin, Xu-an, Zhao
#Algebraic Topology (math.AT) #Combinatorics (math.CO) #FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1210.0648

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× 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\citeKac₈5 and a conjecture of Chapavalov, Leites and Stekolshchik\citeCDR₁0.

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