This article is cited in 3 papers

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

A. N. Leznov<sup>ab

a</sup> 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: 10.4213/tmf601

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

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