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Peterson-type dimension formulas for graded Lie superalgebras

  • Seok-Jin Kang (a1), Jae-Hoon Kwon (a2) and Young-Tak Oh (a3)

Abstract

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.

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References

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Keywords

Peterson-type dimension formulas for graded Lie superalgebras

  • Seok-Jin Kang (a1), Jae-Hoon Kwon (a2) and Young-Tak Oh (a3)

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