Pairings and actions for dynamical quantum groups

Details Pairings and actions for dynamical quantum groups Pairings and actions for dynamical quantum groups

2004-12-10

arxiv.org/abs/math/0412205v1

Adv. Math. 208 (2007), no. 1, 1 - 39

Mathematics

Quantum Algebra

32 pages

Scientific paper

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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