Representations of elliptic quantum groups and their applications to elliptic special functions

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By adding a Hopf algebroid structure to the face type elliptic algebra U_<q,p>(AN^<(1)>), we have formulated it as an elliptic quantum group. Thanks to this structure, we have formulated the intertwining operators on the infinite-dimensional dynamical modules and obtained a consistent result to the previous one derived by using the quasi-Hopf algebra structure. We also have formulated the theta function analogue of the Drinfeld polynomials and shown that they specify the finite-dimensional irreducible dynamical representations uniquely. In the case N=2, we have derived the elliptic analogues of the Clebsch-Gordan coefficients for the tensor product of the finite-dimensional dynamical representations, and shown that they are expressed by using the elliptic hypergeometric series _<12>V_<11>.