SMALL ELLIPTIC QUANTUM GROUP e(tau,gamma)(sl(N))

The small elliptic quantum group e(tau,gamma)(sl(N)), introduced in the paper, is an elliptic dynamical analogue of the universal enveloping algebra U(sl(N)). We define highest weight modules, Verma modules, and contragradient modules over e(tau,gamma)(sl(N)), the dynamical Shapovalov form for e(tau,gamma)(sl(N)), and the contravariant form for highest weight e(tau,gamma)(sl(N))-modules. We show that any finite-dimensional sl(N)-module and any Verma module over sl(N) can be lifted to the corresponding e(tau,gamma)(sl(N))-module on the same vector space. For the elliptic quantum group E-tau,E-gamma(sl(N)) we construct the evaluation morphism E-tau,E-gamma(sl(N)) -> e(tau,gamma)(sl(N)), thus making any e(tau,gamma)(sl(N))-module into an evaluation Ee(tau,gamma)(sl(N))-module.