We introduce a modified affine Hecke algebra $\h{H}^{+}_{q\eta}({l})$ ($\h{H}_{q\eta}({l})$) which depends on two deformation parameters $q$ and $\eta$. When the parameter $\eta$ is equal to zero the algebra $\h{H}_{q\eta=0}(l)$ coincides with the usual affine Hecke algebra $\h{H}_{q}(l)$ of type $A_{l-1}$, if the parameter q goes to 1 the algebra $\h{H}^{+}_{q=1\eta}(l)$ is isomorphic to the degenerate affine Hecke algebra $\Lm_{\eta}(l)$ 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.
@article{hal-00473326,
author = {Tolstoy, V. N. and Ogievetsky, O. V. and Pyatov, P. N. and Isaev, A. P.},
title = {Modified Affine Hecke Algebras and Drinfeldians of Type A},
journal = {HAL},
volume = {1999},
number = {0},
year = {1999},
language = {en},
url = {http://dml.mathdoc.fr/item/hal-00473326}
}
Tolstoy, V. N.; Ogievetsky, O. V.; Pyatov, P. N.; Isaev, A. P. Modified Affine Hecke Algebras and Drinfeldians of Type A. HAL, Tome 1999 (1999) no. 0, . http://gdmltest.u-ga.fr/item/hal-00473326/