Modified Affine Hecke Algebras and Drinfeldians of Type A

We introduce a modified affine Hecke algebra $\text{h}{H}_{q\eta }^{+}(l)$ ($\text{h}{H}_{q\eta }(l)$) which depends on two deformation parameters $q$ and $\eta$. When the parameter $\eta$ is equal to zero the algebra $\text{h}{H}_{q\eta =0}(l)$ coincides with the usual affine Hecke algebra $\text{h}{H}_q(l)$ of type $A_{l-1}$, if the parameter q goes to 1 the algebra $\text{h}{H}_{q=1\eta }^{+}(l)$ is isomorphic to the degenerate affine Hecke algebra ${\text{Lm}}_{\eta }(l)$ introduced by Drinfeld. We construct a functor from a category of representations of $H_{q\eta }^{+}(l)$ into a category of representations of Drinfeldian $D_{q\eta }(sl(n+1))$ which has been introduced by the first author.