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A new approach to the representation theory of semisimple Lie algebras and quantum algebras

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Abstract

We propose a method for explicitly constructing the simple-root generators in an arbitrary finite-dimensional representation of a semisimple quantum algebra or Lie algebra. The method is based on general results from the global theory of representations of semisimple groups. The rank-two algebras A2, B2=C2, D2, and G2 are considered as examples. The simple-root generators are represented as solutions of a system of finite-difference equations and are given in the form of Nl×Nl matrices, where Nl is the dimension of the representation.

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References

  1. H. Weyl,The Classical Groups: Their Invariants and Representations, Princeton Univ. Press, Princeton (1946).

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  2. I. M. Gel’fand and M. L. Tsetlin,Dokl. Acad. Nauk SSSR,71, 825–829 (1950).

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Authors and Affiliations

  1. Institute for High Energy Physics, Protvino, Moscow Oblast, Russia

    A. N. Leznov

  2. Bogoliubov Laboratory of Theoretical Physics, JINR, Dubna, Moscow Oblast, Russia

    A. N. Leznov

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  1. A. N. Leznov
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 123, No. 2, pp. 264–284, May, 2000.

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Leznov, A.N. A new approach to the representation theory of semisimple Lie algebras and quantum algebras. Theor Math Phys 123, 633–650 (2000). https://doi.org/10.1007/BF02551396

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  • DOI: https://doi.org/10.1007/BF02551396

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