Primitive vectors of Kac-modules of the Lie superalgebras sl(m/n)

Journal of Mathematical Physics

Volumn 41, Issue 7, 2000, Pages 5064-5087

  Su, Yucai ^b   Hughes, J W B ^a   King, R C ^b  

^a QUEEN MARY UNIVERSITY OF LONDON   (United Kingdom)

^b NONE

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0034415798     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.533392     Document Type: Article

References (20)

1. V. G. Kac, "Classification of simple Lie superalgebras," Funct. Anal. Appl. 9, 263-265 (1975).
2. V. G. Kac, "Lie superalgebras," Adv. Math. 26, 8-96 (1977).
3. M. Scheunert, The Theory of Lie Superalgebras (Springer, Berlin, 1979).
4. V. G. Kac, "Characters of typical representations of classical Lie superalgebras," Commun. Alg. 5, 889-897 (1977).
5. V. G. Kac, "Representations of classical Lie superalgebras," Lect. Notes Math. 676, 597-626 (1978).
6. J. Van der Jeugt, J. W. B. Hughes, R. C. King, and J. Thierry-Mieg, "Character formulas for irreducible modules of the Lie superalgebra sl(m/n)," J. Math. Phys. 31, 2278-2304 (1990).
7. J. Van der Jeugt, J. W. B. Hughes, R. C. King, and J. Thierry-Mieg, "A character formula for singly atypical modules of the Lie superalgebra sl(m/n)," Commun. Alg. 19, 199-222 (1991).
8. J. W. B. Hughes, R. C. King, and J. Van der Jeugt, "On the composition factors of Kac modules for the Lie superalgebra sl(m/n)," J. Math. Phys. 33, 470-491 (1992).
9. H. Shakibi, "Kac modules of sl(2/2) and the extended Kac-Weyl formula," Mathematika 39, 37-48 (1992).
10. H. Shakibi, "Composition factors of the Kac module for the Lie superalgebras sl(3/3) and sl(r/r)," Commun. Alg. 21, 3099-3126 (1993).
11. H. Shakibi, "Composition factors of the Kac module for critical highest weights of sl(m/n)," Commun. Alg. 21, 3127-3134 (1993).
12. H. Shakibi, "Infinite and finite-dimensional representations of the Lie superalgebra sl(m/n)," Commun. Alg. 22, 951-967 (1994).
13. V. Serganova, "Kazhdan-Lusztig polynomials and character formula for the Lie superalgebra gl(m/n)," Selecta Mathematica 2, 607-651 (1996).
14. J. Van der Jeugt and R. B. Zhang, "Characters and composition factor multiplicities for the Lie superalgebra gl(m/n)," Lett. Math. Phys. 47, 49-61 (1999).
15. T. D. Palev, "Finite-dimensional representations of the special linear Lie superalgebra sl(1,n). II. Nontypical representations," J. Math. Phys. 29, 2589-2598 (1988).
16. T. D. Palev, "Essentially typical representations of the Lie superalgebras gl(n/m) in a Gel'fand-Zetlin basis," Funct. Anal. Appl. 23, 141-142 (1989) (English translation).
17. Y.-C. Su, "Classification of finite dimensional modules of the Lie superalgebra sl(2/1)," Commun. Alg. 20, 3259-3277 (1992).
18. J. Germoni, "Indecomposable representations of special linear Lie superalgebras," J. Alg. 209, 367-401 (1998).
19. Y.-C. Su, "Weakly primitive vectors of Kac-modules of the Lie superalgebras sl(m/n)," submitted to J. Math. Phys.
20. V. G. Kac, Infinite Dimensional Lie Algebras, 3rd ed. (Cambridge University Press, Cambridge, 1990).