Gelfand-Tsetlin bases for classical Lie algebras
By Alexander I. Molev. 2002
166 citations recorded by the source corpus.
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
Subfields: Algebra and Number Theory, Geometry and Topology, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/df5f8edff5948b645b0b00f46744655dafc11d42
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In Algebra and Number Theory
In Geometry and Topology
- Roman Lavicka
- Andrei Neguț
- V. Souček
- K. Guerlebeck
- L. Rybnikov
- Michael Finkelberg
- Boris Feigin
- S. Bock
In Statistical and Nonlinear Physics
Citations in the corpus
- Yangians and cohomology rings of Laumon spaces (2008, methodology): “We will follow the notations of [14] on the Gelfand-Tsetlin bases in representations of gln.”
- The Gelfand-Tsetlin bases for spherical monogenics in dimension 3 (2010, background): “The notion of a Gelfand–Tsetlin basis (GT basis) was formulated for irreducible (finite dimensional) modules over a general classical simple Lie algebra g (see [27] for the original paper, and [37] for a review paper with many further references).”
- Complete Orthogonal Appell Systems for Spherical Monogenics (2011, background): “Gelfand-Tsetlin bases for spin modules Now we recall an abstract definition of a Gelfand-Tsetlin basis for any given irreducible finite dimensional Spin(m)-module V (see [17, 24]).”