In:
Nagoya Mathematical Journal, Cambridge University Press (CUP), Vol. 163 ( 2001-09), p. 107-144
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 × Z 2 )-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.
Type of Medium:
Online Resource
ISSN:
0027-7630
,
2152-6842
DOI:
10.1017/S0027763000007935
Language:
English
Publisher:
Cambridge University Press (CUP)
Publication Date:
2001
detail.hit.zdb_id:
2186888-8
SSG:
17,1
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