  Recently N.Jing discovered a certain combinatorial identity from validity of
the Serre relations in some vertex representations of quantum Kac-Moody
algebras.
  We generalize this identity, in particular, extending it from polynomials to
elliptic functions, and interprete the obtained identities in terms of tensor
products of evaluation representations of the quantum loop algebra
$U_q(\tilde{gl_2})$ or the elliptic quantum group $E_{\rho,\gamma}(sl_2)$.
