Tensor Product Representation

Abstract

In this chapter, we discuss a tensor product representation of the n evaluation representations constructed in Chap. 4. We introduce the Gelfand-Tsetlin basis of the tensor product space and construct an action of the elliptic currents and the half currents of \(U_{q,p}(\widehat {\mathfrak {sl}}_2)\) on it. Remarkably, the change of basis matrix from the standard basis to the Gelfand-Tsetlin basis is given by a specialization of the elliptic weight functions. The resultant action is expressed in a perfectly combinatorial way in terms of the partitions of [1, n]. In Chap. 9 we discuss a geometric interpretation of it.