SIMPLE BOUNDED HIGHEST WEIGHT MODULES OF BASIC CLASSICAL LIE SUPERALGEBRAS

We classify all simple bounded highest weight modules of a basic classical Lie superalgebra g . In particular, our result leads to the classification of the simple weight modules with finite weight multiplicities over all classical Lie superalgebras. We also obtain some character formulas of strongl...

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Bibliographic Details
Published inTransformation groups Vol. 26; no. 3; pp. 893 - 914
Main Authors GORELIK, MARIA, GRANTCHAROV, DIMITAR
Format Journal Article
LanguageEnglish
Published New York Springer US 01.09.2021
Springer Nature B.V
Subjects
Algebra
Lie Groups
Mathematics
Mathematics and Statistics
Modules
Topological Groups
Weight
odd reflections
Primary: 17B10
Lie superalgebras
weight modules
character formulas
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Summary:We classify all simple bounded highest weight modules of a basic classical Lie superalgebra g . In particular, our result leads to the classification of the simple weight modules with finite weight multiplicities over all classical Lie superalgebras. We also obtain some character formulas of strongly typical bounded highest weight modules of g .
ISSN:1083-4362
1531-586X
DOI:10.1007/s00031-020-09616-x