Nonclassical type representations of the q-deformed algebra $U'_q({\rm so}_n)$

Details Nonclassical type representations of the q-deformed algebra $U'_q({\rm so}_n)$ Nonclassical type representations of the q-deformed algebra $U'_q({\rm so}_n)$

1999-11-17

arxiv.org/abs/math/9911129v1

Mathematics

Quantum Algebra

6 pages, LaTeX

Scientific paper

10.1023/A:1022877015703

The nonstandard q-deformation $U'_q({\rm so}_n)$ of the universal enveloping algebra $U({\rm so}_n)$ has irreducible finite dimensional representations which are a q-deformation of the well-known irreducible finite dimensional representations of $U({\rm so}_n)$. But $U'_q({\rm so}_n)$ also has irreducible finite dimensional representations which have no classical analogue. The aim of this paper is to give these representations which are called nonclassical type representations. They are given by explicit formulas for operators of the representations corresponding to the generators of $U'_q({\rm so}_n)$.

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