The algebra Uq(sl2) in disguise

We discuss a connection between the algebra Uq(sl2) and the tridiagonal pairs of q-Racah type. To describe the connection, let x, y±1, z denote the equitable generators for Uq(sl2). Let Uq∨ denote the subalgebra of Uq(sl2) generated by x, y−1, z. Using a tridiagonal pair of q-Racah type we construct two finite-dimensional Uq∨-modules. The constructions yield two nonstandard presentations of Uq∨ by generators and relations. These presentations are investigated in detail.