Communications in Mathematical Physics

, Volume 201, Issue 3, pp 591–618

A Basis for Representations of Symplectic Lie Algebras

  • A. I. Molev

DOI: 10.1007/s002200050570

Cite this article as:
Molev, A. Comm Math Phys (1999) 201: 591. doi:10.1007/s002200050570


A basis for each finite-dimensional irreducible representation of the symplectic Lie algebra ??(2n) is constructed. The basis vectors are expressed in terms of the Mickelsson lowering operators. Explicit formulas for the matrix elements of generators of ??(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 ??(2n− 2) highest vectors in any finite-dimensional irreducible representation of ??(2n) admits a natural structure of a representation of the Yangian Y(??(2)).

Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • A. I. Molev
    • 1
  1. 1.School of Mathematics and Statistics, University of Sydney, Sydney NSW 2006, Australia.¶ E-mail: