Vertex-IRF transformations, dynamical quantum groups and harmonic analysis

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 Koornwinders 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.

Author: Jasper V. Stokman

Source: https://archive.org/