On Gelfand-Tsetlin Bases for Representations of Classical Lie Algebras

A. I. Molev ()
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A. I. Molev: University of Sydney, School of Mathematics and Statistics

A chapter in Formal Power Series and Algebraic Combinatorics, 2000, pp 300-308 from Springer

Abstract: Abstract We construct a weight basis for each finite-dimensional irreducible representation of the simple complex Lie algebra g n of type B n , C n , or D n . We derive explicit formulas for the matrix elements of generators of the Lie algebra in this basis. The basis vectors are parameterized by the Gelfand-Tsetlin patterns associated with the chain of subalgebras g1 ⊂ g2 ⊂ … ⊂ gn. The construction is based on the representation theory of the Yangians.

Date: 2000
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-662-04166-6_27

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DOI: 10.1007/978-3-662-04166-6_27

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