  We propose a new realization of the elliptic quantum group equipped with the
H-Hopf algebroid structure on the basis of the elliptic algebra
U_{q,p}(\hat{sl}_2). The algebra U_{q,p}(\hat{sl}_2) has a constructive
definition in terms of the Drinfeld generators of the quantum affine algebra
U_q(\hat{sl}_2) and a Heisenberg algebra. This yields a systematic construction
of both finite and infinite-dimensional dynamical representations and their
parallel structures to U_q(\hat{sl}_2). In particular we give a classification
theorem of the finite-dimensional irreducible pseudo-highest weight
representations stated in terms of an elliptic analogue of the Drinfeld
polynomials. We also investigate a structure of the tensor product of two
evaluation representations and derive an elliptic analogue of the
Clebsch-Gordan coefficients. We show that it is expressed by using the
very-well-poised balanced elliptic hypergeometric series 12V11.
