  We construct a fully faithful functor from the category C_F of
finite-dimensional representations of Felder's (dynamical) elliptic quantum
group E_{tau,gamma}(gl(n)) to a cretain category D_B of (infinite-dimensional)
representations of Belavin's quantum elliptic algebra B by difference
operators, and a fully faithful functor from the category C_B of
finite-dimensional representations of B to D_B. As a corollary, we show that
the abelian subcategories of C_B and C_F generated by tensor products of vector
representations are equivalent.
