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Highest-weight representations of the sl (n+ 1, C) algebras: Maximal representations

C Burdik M Havlicek Pavel Exner

TBD mathscidoc:1910.43227

Journal of Physics A: Mathematical and General, 14, (5), 1039, 1981.5
Representations of the sl (n+ 1, C) Lie algebras are constructed with the help of canonical (boson) realisations of these algebras. For every weight Lambda on the standard Cartan subalgebra of sl (n+ 1, C) the authors obtain a representation rho Lambda (n+ 1)(called the maximal representation) which contains an irreducible subrepresentation with Lambda as the highest weight. It is shown that for a major part of the weights Lambda the representations rho Lambda (n+ 1) themselves are irreducible. The standard construction of the highest-weight representations of semi-simple Lie algebras is based on the so-called elementary representations; comparing with them, the authors maximal representations are given in the explicit form.
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@inproceedings{c1981highest-weight,
  title={Highest-weight representations of the sl (n+ 1, C) algebras: Maximal representations},
  author={C Burdik, M Havlicek, and Pavel Exner},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020133929565044756},
  booktitle={Journal of Physics A: Mathematical and General},
  volume={14},
  number={5},
  pages={1039},
  year={1981},
}
C Burdik, M Havlicek, and Pavel Exner. Highest-weight representations of the sl (n+ 1, C) algebras: Maximal representations. 1981. Vol. 14. In Journal of Physics A: Mathematical and General. pp.1039. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020133929565044756.
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