Gelfand-Tsetlin bases for classical Lie algebras

Abstract

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

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

References in corpus (4)

• q-Deformed Orthogonal and Pseudo-Orthogonal Algebras and Their Representations
• Representations of twisted Yangians associated with skew Young diagrams
• Representations of Yangians associated with skew Young diagrams
• An algorithm for computing the global basis of an irreducible $U_q(s{p}_{2n})$-module

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