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Pairings and actions for dynamical quantum groups

Erik Koelink·Yvette van Norden
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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.

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Erik Koelink, Yvette van Norden. 2004-12-10. Pairings and actions for dynamical quantum groups. https://arxiv.org/abs/math/0412205

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