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TMF, 2000, Volume 123, Number 2, Pages 264–284 (Mi tmf601)  

This article is cited in 3 scientific papers (total in 3 papers)

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

A. N. Leznovab

a Institute for High Energy Physics
b Joint Institute for Nuclear Research, Bogoliubov Laboratory of Theoretical Physics

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 $A_2$, $B_2=C_2$, $D_2$, and $G_2$ 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 $N_l\times N_l$ matrices, where $N_l$ is the dimension of the representation.

DOI: https://doi.org/10.4213/tmf601

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English version:
Theoretical and Mathematical Physics, 2000, 123:2, 633–650

Bibliographic databases:


Citation: A. N. Leznov, “A new approach to the representation theory of semisimple Lie algebras and quantum algebras”, TMF, 123:2 (2000), 264–284; Theoret. and Math. Phys., 123:2 (2000), 633–650

Citation in format AMSBIB
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\paper A new approach to the representation theory of semisimple Lie algebras and quantum algebras
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\yr 2000
\vol 123
\issue 2
\pages 264--284
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\crossref{https://doi.org/10.4213/tmf601}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1794159}
\zmath{https://zbmath.org/?q=an:1035.17012}
\transl
\jour Theoret. and Math. Phys.
\yr 2000
\vol 123
\issue 2
\pages 633--650
\crossref{https://doi.org/10.1007/BF02551396}
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. N. Leznov, “Invariant Form of the Generators of Semisimple Lie and Quantum Algebras in Their Arbitrary Finite-Dimensional Representation”, Theoret. and Math. Phys., 126:3 (2001), 307–325  mathnet  crossref  crossref  mathscinet  zmath  isi
    2. Leznov, AN, “Fine structure of the discrete transformation for multicomponent integrable systems”, Journal of Nonlinear Mathematical Physics, 10:2 (2003), 243  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus  scopus
    3. Leznov, AN, “Discrete transformation for the matrix three-wave problem in three dimensional space”, Journal of Mathematical Physics, 44:5 (2003), 2342  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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