Hostname: page-component-78c5997874-lj6df Total loading time: 0 Render date: 2024-11-05T13:16:43.349Z Has data issue: false hasContentIssue false
  • English
  • Français

Tableaux Realization of Generalized Verma Modules

Published online by Cambridge University Press:  20 November 2018

Volodymyr Mazorchuk
Volodymyr Mazorchuk*
Affiliation:
Mechanics and Mathematics Department, Kyiv Taras Shevchenko University, 64, Volodymyrska st. 252033 Kyiv, Ukraine
*
e-mail: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We construct the tableaux realization of generalized Verma modules over the Lie algebra $\text{sl(3,}\,\mathbb{C})$. By the same procedure we construct and investigate the structure of a new family of generalized Verma modules over $\text{sl(}n,\,\mathbb{C}\text{)}$.

Keywords

17B3517B10
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 50 , Issue 4 , 01 August 1998 , pp. 816 - 828
Copyright
Copyright © Canadian Mathematical Society 1998

References

1. Barut, A. O. and Raczka, R., Theory of group representations and applications. PWN, Polish Scientific Publisher, Warszawa, 1977.Google Scholar
2. Coleman, A. J., Futorny, V. M., Stratified L-modules. J. Algebra 163(1994), 219–234.Google Scholar
3. Dixmier, J., Enveloping algebras. North-Holland, Amsterdam, 1977.Google Scholar
4. Yu. Drozd, A., Ovsienko, S. A. and Futorny, V. M., Harish-Chandra Subalgebras and Gelfand-Zetlin modules. J. Math. Phys. Sci. 424(1994).Google Scholar
5. Yu. Drozd, A., S-homomorphism of Harish-Chandra and -modules generated by semiprimitive elements. Ukrainian Math. J. 42(1990), 1032–1037.Google Scholar
6. Futorny, V. and Mazorchuk, V., Structure ofα-stratified modules for finite-dimensional Lie algebras, I. J. Algebra 183(1996), 456–482.Google Scholar
7. Futorny, V. M., Weightsl(3)-modules, generated by semiprimitive element. UkrainianMath. J. 43(1991), 281–285.Google Scholar
8. Futorny, V. M., A generalization of Verma modules and irreducible representations of the Lie algebrasl(3ÒC). Ukrainian Math. J. 38(1986), 422–427.Google Scholar
9. Gelfand, I. M. and Zetlin, M. L., Finite-dimensional representations of a Group of unimodular matrices. Dokl. Akad. Nauk SSSR 8–25 71(1950), 825–828 (in Russian).Google Scholar
10. Gelfand, I. M., Finite-dimensional representations of Groups of orthogonal matrices. Dokl. Akad. Nauk SSSR 71(1950), 1017–1020 (in Russian).Google Scholar
11. Kostant, B., On the tensor product of a finite and infinite dimensional representations. J. Funct. Anal. 20(1975), 257–285.Google Scholar
12. Mazorchuk, V. and Ovsienko, S., Submodule structure of generalized Vermamodules induced from generic Gelfand-Zetlin modules. Bielefeld University, 97–007, preprintGoogle Scholar
13. Rocha-Caridi, A., Splitting criteria for -modules induced from a parabolic and a Bernstein-Gelfand- Gelfand resolution of a finite-dimensional, irreducible -module. Trans. Amer. Math. Soc. 262(1980), 335 366.Google Scholar
14. Zelobenko, D. P., Compact Lie groups and their representations. Nauka, Moskow, 1974.Google Scholar