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On Gelfand-Tsetlin Bases for Representations of Classical Lie Algebras

In: Formal Power Series and Algebraic Combinatorics

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  • A. I. Molev

    (University of Sydney, School of Mathematics and Statistics)

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.

Suggested Citation

  • A. I. Molev, 2000. "On Gelfand-Tsetlin Bases for Representations of Classical Lie Algebras," Springer Books, in: Daniel Krob & Alexander A. Mikhalev & Alexander V. Mikhalev (ed.), Formal Power Series and Algebraic Combinatorics, pages 300-308, Springer.
    • Handle: RePEc:spr:sprchp:978-3-662-04166-6_27
    DOI: 10.1007/978-3-662-04166-6_27
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