Back to Search
Start Over
Peterson-type dimension formulas for graded Lie superalgebras
- Source :
- Nagoya Math. J. 163 (2001), 107-144
- Publication Year :
- 2001
- Publisher :
- Cambridge University Press (CUP), 2001.
-
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.
- Subjects :
- General Mathematics
Simple Lie group
Mathematics::Rings and Algebras
010102 general mathematics
Mathematical analysis
Dimension (graph theory)
Adjoint representation
Lie superalgebra
11F22
Type (model theory)
01 natural sciences
Free abelian group
Graded Lie algebra
Combinatorics
High Energy Physics::Theory
Representation of a Lie group
Mathematics::Quantum Algebra
17B70
0101 mathematics
Mathematics::Representation Theory
Mathematics
Subjects
Details
- ISSN :
- 21526842 and 00277630
- Volume :
- 163
- Database :
- OpenAIRE
- Journal :
- Nagoya Mathematical Journal
- Accession number :
- edsair.doi.dedup.....fadf7580207c605b7e686235f148a03c