Vertex-IRF transformations, dynamical quantum groups and harmonic analysis

Details Vertex-IRF transformations, dynamical quantum groups and harmonic analysis Vertex-IRF transformations, dynamical quantum groups and harmonic analysis

2003-05-23

arxiv.org/abs/math/0305324v1

Mathematics

Quantum Algebra

24 pages

Scientific paper

It is shown that a dynamical quantum group arising from a vertex-IRF transformation has a second realization with untwisted dynamical multiplication but nontrivial bigrading. Applied to the $\hbox{SL}(2;\mathbb{C})$ dynamical quantum group, the second realization is naturally described in terms of Koornwinder's twisted primitive elements. This leads to an intrinsic explanation why harmonic analysis on the ``classical'' $\hbox{SL}(2;\mathbb{C})$ quantum group with respect to twisted primitive elements, as initiated by Koornwinder, is the same as harmonic analysis on the $\hbox{SL}(2;\mathbb{C})$ dynamical quantum group.

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