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Peterson-type dimension formulas for graded Lie superalgebras

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Authors
Kang, Seok-Jin; Kwon, Jae-Hoon; Oh, Young-Tak
Issue Date
2001
Publisher
Nagoya University, Graduate School of Mathematics
Citation
Nagoya Math. J., 163 (2001), 107-144
Keywords
Peterson-type dimension formulasgraded Lie superalgebras
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 $\fL=\bigoplus_{(\alpha, a) \in \Gamma \times \Z_2} {\fL}_{(\alpha, a)}$ be a ($\Gamma\times\Z_{2}$)-graded Lie superalgebra. In this paper, by applying formal differential operators and the Laplacian to the denominator identity of $\fL$, we derive a new recursive formula for the dimensions of homogeneous subspaces of $\fL$. 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.
ISSN
0027-7630
Language
English
URI
https://hdl.handle.net/10371/12197
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College of Natural Sciences (자연과학대학)Dept. of Mathematical Sciences (수리과학부)Journal Papers (저널논문_수리과학부)
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