Gelfand-Tsetlin bases for classical Lie algebras

Details Gelfand-Tsetlin bases for classical Lie algebras Gelfand-Tsetlin bases for classical Lie algebras

2002-11-19

arxiv.org/abs/math/0211289v2

in "Handbook of Algebra", Vol. 4, (M. Hazewinkel, Ed.), Elsevier, 2006, pp. 109-170

Mathematics

Representation Theory

65 pages, bibliography is extended, minor corrections and changes are made

Scientific paper

This is a review paper on the Gelfand-Tsetlin type bases for representations of the classical Lie algebras. Different approaches to construct the original Gelfand-Tsetlin bases for representations of the general linear Lie algebra are discussed. Weight basis constructions for representations of the orthogonal and symplectic Lie algebras are reviewed. These rely on the representation theory of the B,C,D type twisted Yangians

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