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2001 Peterson-type dimension formulas for graded Lie superalgebras
Seok-Jin Kang, Jae-Hoon Kwon, Young-Tak Oh
Nagoya Math. J. 163: 107-144 (2001).

Abstract

Let $\widehat {\Gamma}$ be a free abelian group of finite rank, let $\Gamma$ be a sub-semigroup of $\widehat {\Gamma}$ satisfying certain finiteness conditions, and let $\mathfrak{L}=\bigoplus_{(\alpha, a) \in \Gamma \times \mathbb{Z}_2} \mathfrak{L}_{(\alpha, a)}$ be a ($\Gamma\times\mathbb{Z}_{2}$)-graded Lie superalgebra. In this paper, by applying formal differential operators and the Laplacian to the denominator identity of $\mathfrak{L}$, we derive a new recursive formula for the dimensions of homogeneous subspaces of $\mathfrak{L}$. When applied to generalized Kac-Moody superalgebras, our formula yields a generalization of Peterson's root multiplicity formula. We also obtain a Freudenthal-type weight multiplicity formula for highest weight modules over generalized Kac-Moody superalgebras.

Citation

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Seok-Jin Kang. Jae-Hoon Kwon. Young-Tak Oh. "Peterson-type dimension formulas for graded Lie superalgebras." Nagoya Math. J. 163 107 - 144, 2001.

Information

Published: 2001
First available in Project Euclid: 27 April 2005

zbMATH: 1054.17023
MathSciNet: MR1855192

Subjects:
Primary: 17B70
Secondary: 11F22

Rights: Copyright © 2001 Editorial Board, Nagoya Mathematical Journal

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Vol.163 • 2001
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