Pairings and actions for dynamical quantum groups

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, corepresentations and dynamical representations is studied, and natural left and right actions are introduced. Explicit details for the elliptic U(2) dynamical quantum group 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.