The algebra Uq(sl2) in disguise

We discuss a connection between the algebra U-q(sl(2)) and the tridiagonal pairs of q-Racah type. To describe the connection, let x, y(+/- 1), z denote the equitable generators for U-q(sl(2)). Let U-q(V) denote the subalgebra of U-q(sl(2)) generated by x, y(-1), z. Using a tridiagonal pair of q-Racah type we construct two finite-dimensional U-q(V)-modules. The constructions yield two nonstandard presentations of U-q(V) by generators and relations. These presentations are investigated in detail. (C) 2014 Elsevier Inc. All rights reserved.