The torsion free Pieri formula

Canadian Journal of Mathematics

Volumn 50, Issue 2, 1998, Pages 266-289

  Britten, D J ^a   Lemire, F W ^a  

^a UNIVERSITY OF WINDSOR   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0032382909     PISSN: 0008414X     EISSN: None     Source Type: Journal    
DOI: 10.4153/CJM-1998-014-8     Document Type: Article

References (18)

1. G. M. Benkart, D. J. Britten and F. W. Lemire, Stability in Modules for Classical Lie Algebras - A Constructive Approach. Mem. Amer. Math. Soc. 85(1990).
2. G. M. Benkart, D. J. Britten and F. W. Lemire, Modules with Bounded Weight Multiplicities for Simple Lie Algebras. Math. Z., to appear.
3. 2 modules with a finite dimensional weight space. Comm. Algebra 23(1995), 467-510.
4. n-modules with multiplicities 1 and applications. Canad. J. Phys. 72(1994), 326-335.
5. D. J. Britten and F. W. Lemire, A classification of simple Lie modules having a 1-dimensional weight space. Trans. Amer. Math. Soc. 299(1987), 683-697.
6. n. Canad. J. Math. 37(1985), 122-140.
7. 2-modules having a 1-dimensional weight space. M. Sc. Thesis, University of Windsor, Windsor, Ontario, 1995.
8. J. Dixmier, Algèbres Enveloppantes. Gauthier-Villars, Paris, Brussels, Montréal, 1974.
9. Y. A. Drozd, S. A. Ovsienko and V. M. Futomy, On Gel'fand-Zetlin Modules. Proc. of the Winter School on Geometry and Physics, Series II 26(1991), 143-147.
10. M. Duflo, Sur la classification des idéaux primitifs dans l'algèbre enveloppante d'une algèbre de Lie semi-simple. Ann. of Math. 105(1977), 107-120.
11. S. L. Fernando, Lie algebra modules with finite dimensional weight spaces I. Trans. Amer. Math. Soc. 322(1990), 757-781.
12. W. Fulton and J. Harris, Representation Theory - A First Course. Graduate Texts in Math. 129, Springer-Verlag, New York, 1991.
13. J. E. Humphreys, Introduction to Lie Algebras and Representation Theory. Graduate Texts in Math. 9. Springer-Verlag, New York, 1972.
14. B. Kostant, On the tensor product of a finite and an infinite dimensional representation. J. Funct. Anal. 20(1975), 257-285.
15. F. W. Lemire, Irreducible representations of a simple Lie algebra admitting a one-dimensional weight space. Proc. Amer. Math. Soc. 19(1968), 1161-1164.
16. _, Weight Spaces and Irreducible Representations of Simple Lie Algebras. Proc. Amer. Math. Soc. 22(1969), 192-197.
17. _, One dimensional representations of the cycle subalgebra of a semisimple Lie algebra. Canad. Math. Bull. 13(1970), 463-467.
18. D. P. Zelobenko, Compact Lie Groups and their Representations. Translations of Math. Monographs 40, Amer. Math. Soc., Providence, Rhode Island, 1973.