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 Uq,p(sl2) 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.