A Basis for Representations of Symplectic Lie Algebras

Details A Basis for Representations of Symplectic Lie Algebras A Basis for Representations of Symplectic Lie Algebras

1998-04-27

arxiv.org/abs/math/9804127v1

Comm. Math. Phys. 201 (1999), 591--618.

Mathematics

Quantum Algebra

34 pages, AmSTeX

Scientific paper

10.1007/s002200050570

A basis for each finite-dimensional irreducible representation of the symplectic Lie algebra sp(2n) is constructed. The basis vectors are expressed in terms of the Mickelsson lowering operators. Explicit formulas for the matrix elements of generators of sp(2n) in this basis are given. The basis is natural from the viewpoint of the representation theory of the Yangians. The key role in the construction is played by the fact that the subspace of sp(2n-2)-highest vectors in any finite-dimensional irreducible representation of sp(2n) admits a natural structure of a representation of the Yangian Y(gl(2)).

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