Skip to main content Accessibility help
×
Home

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

  • H. Shakibi (a1)

Extract

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).

Copyright

References

Hide All
[Kl]Kac, V. G., Representations of Classical Lie Superalgebras, Lecture Notes in Mathematics 676, 579626, eds Bleuler, K., Petry, H. and Reetz, A. (Springer, Berlin, 1977).
[K2]Kac, V. G., Lie superalgebras, Adv. Math., 26 (1977) 896.
[VHKT1]Jeugt, J. Van der, Hughes, J. W. B., King, R. C. and Thierry-Mieg, J., A character formula for singly atypical modules of the Lie superalgebra s1 (m/n), Commun. Alg., 18(10) (1990) 34533480.
[VHKT2]Jeugt, J. Van der, Hughes, J. W. B., King, R. C. and Thierry-Mieg, J., Character formulae for irreducible modules of the Lie superalgebra s1 (m/n), J. Math. Phys., 31 (1990) 2278.
[PS]Palev, T. D. and Stoilova, N. I., Finite-dimensional representations of the Lie superalgebra gl (2/2) in a gl (2) ⊕ gl (2) basis. II. Nontypical representations, J. Math. Phys., 31 (1990) 953.
[HKV]Hughes, J. W. B., King, R. C., Jeugt, J. Van der, On the composition factors of the Kac module V(Λ) for the Lie superalgebra s1(m/n), J. Math. Phys., 33 (1992), 470491.
[BL]Bernstein, I. N. and Leites, D. A., A formula for the characters of the irreducible finite-dimensional representations of Lie superalgebras of series gl and s1. C.R. Acad. Bulg. Sci., 33 (1980) 10491051 (in Russian).
[S]Shakibi, H., A study of Kac modules for Lie superalgebras of type s1 (m/n), Ph.D. Thesis (Queen Mary and Westfield College, 1992).
MathJax
MathJax is a JavaScript display engine for mathematics. For more information see http://www.mathjax.org.

MSC classification

Related content

Powered by UNSILO

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

  • H. Shakibi (a1)

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed.