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Kac modules of sl (2/2) and the extended Kac-Weyl formulas

Part of: Jordan algebras

Published online by Cambridge University Press:  26 February 2010

H. Shakibi
H. Shakibi
Affiliation:
School of Mathematical Sciences, Queen Mary and Westfield College, Mile End Road, London. El 4NS
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Abstract. We consider the structure of the Kac modules V(Λ) for dominant integral doubly atypical weights Λ of the Lie superalgebra s1(2/2). Primitive vectors of V(Λ) are constructed and it is shown that the number of composition factors of V(Λ) for such Λ is in exact agreement with the conjectures of [HKV]. These results are used to show that the extended Kac-Weyl character formula which was proved in [VHKTl] for singly atypical simple modules of s1(m/n), and conjectured to be valid for all finite dimensional irreducible representations of sl(m/n) in [VHKT2] is in fact valid for all finite-dimensional doubly atypical simple modules of s1(2/2).

MSC classification

Secondary: 17C70: Super structures

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Type
Research Article
Information
Mathematika , Volume 39 , Issue 1 , June 1992 , pp. 37 - 48
Copyright
Copyright © University College London 1992

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References

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