Quantum Script W sign-algebras and elliptic algebras

We define a quantum Script W sign-algebra associated to sl_N as an associative algebra depending on two parameters. For special values of the parameters, this algebra becomes the ordinary Script W sign-algebra of sl_N, or the q-deformed classical Script W sign-algebra of sl_N. We construct free field realizations of the quantum Script W sign-algebras and the screening currents. We also point out some interesting elliptic structures arising in these algebras. In particular, we show that the screening currents satisfy elliptic analogues of the Drinfeld relations in Uq(n̂).