English

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}
}

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32 pages