Pairings and actions for dynamical quantum groups
Quantum Algebra
2010-10-25 v1
Abstract
Dynamical quantum groups constructed from a FRST-construction using a solution of the quantum dynamical Yang-Baxter equation are equipped with a natural pairing. The interplay of the pairing with *-structures, (unitarizable) corepresentations and dynamical representations is studied, and natural left and right actions are introduced. Explicit details for the elliptic U(2) dynamical quantum group corresponding to the elliptic R-matrix for sl(2) are given, and the pairing is calculated explicitly in terms of elliptic hypergeometric functions. Dynamical analogues of spherical and singular vectors for corepresentations are introduced.
Keywords
Cite
@article{arxiv.math/0412205,
title = {Pairings and actions for dynamical quantum groups},
author = {Erik Koelink and Yvette van Norden},
journal= {arXiv preprint arXiv:math/0412205},
year = {2010}
}
Comments
32 pages