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

Amadou Keita
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Amadou Keita: Department of Mathematics, University of The Gambia, P.O. Box 3530, The Gambia

Academic Journal of Applied Mathematical Sciences, 2021, vol. 7, issue 1, 60-65

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.

Keywords: Finite-dimensional; Module; Irreducible; Representation; Monomial basis. (search for similar items in EconPapers)
Date: 2021
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Handle: RePEc:arp:ajoams:2021:p:60-65