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Peterson-type dimension formulas for graded Lie superalgebras

DC Field Value Language
dc.contributor.authorKang, Seok-Jin-
dc.contributor.authorKwon, Jae-Hoon-
dc.contributor.authorOh, Young-Tak-
dc.date.accessioned2009-11-16T04:38:12Z-
dc.date.available2009-11-16T04:38:12Z-
dc.date.issued2001-
dc.identifier.citationNagoya Math. J., 163 (2001), 107-144en
dc.identifier.issn0027-7630-
dc.identifier.urihttps://hdl.handle.net/10371/12197-
dc.description.abstractLet $\widehat {\Gamma}$ 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.en
dc.language.isoen-
dc.publisherNagoya University, Graduate School of Mathematicsen
dc.subjectPeterson-type dimension formulasen