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Simple Finite-Dimensional Modules and Monomial Bases from the Gelfand-Testlin Patterns

Author

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  • Amadou Keita

    (Department of Mathematics, University of The Gambia, P.O. Box 3530, The Gambia)

Abstract

One of the most important classes of Lie algebras is sl_n, which are the n×n matrices with trace 0. The representation theory for sl_n has been an interesting research area for the past hundred years and in it, the simple finite-dimensional modules have become very important. They were classified and Gelfand and Tsetlin actually gave an explicit construction of a basis for every simple finite-dimensional module. This paper extends their work by providing theorems and proofs and constructs monomial bases of the simple module.

Suggested Citation

  • Amadou Keita, 2021. "Simple Finite-Dimensional Modules and Monomial Bases from the Gelfand-Testlin Patterns," Academic Journal of Applied Mathematical Sciences, Academic Research Publishing Group, vol. 7(1), pages 60-65, 01-2021.
    • Handle: RePEc:arp:ajoams:2021:p:60-65
    DOI: 10.32861/ajams.71.60.65
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