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Peterson-type dimension formulas for graded Lie superalgebras

Published online by Cambridge University Press:  22 January 2016

Seok-Jin Kang ,
Jae-Hoon Kwon  and
Young-Tak Oh
Seok-Jin Kang
Affiliation:
Korea Institute for Advanced Study, 207-43 Cheongryangri-dong, Dongdaemun-gu, Seoul 130-012, Korea, sjkang@kias.re.kr
Jae-Hoon Kwon
Affiliation:
Korea Institute for Advanced Study, 207-43 Cheongryangri-dong, Dongdaemun-gu, Seoul 130-012, Korea, jhkwon@math.snu.ac.kr
Young-Tak Oh
Affiliation:
Department of Mathematics, Seoul National University, Seoul 151-742, Korea, ohyt@math.snu.ac.kr
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Abstract

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Let be a free abelian group of finite rank, let Γ be a sub-semigroup of satisfying certain finiteness conditions, and let be a (Γ × Z2)-graded Lie superalgebra. In this paper, by applying formal differential operators and the Laplacian to the denominator identity of , we derive a new recursive formula for the dimensions of homogeneous subspaces of . 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.

Keywords

17A7017B0117B6517B7011F0311F22
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 163 , September 2001 , pp. 107 - 144
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2000

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