QUANTUM W-ALGEBRAS AND ELLIPTIC ALGEBRAS

We define a quantum W-algebra associated to s(1)N as an associative al gebra depending on two parameters. For special values of the parameter s, this algebra becomes the ordinary W-algebra of s1(N) or the q-defor med classical W-algebra of s1(N). We construct free field realizations of the quantum W-algebras and the screening currents. We also point o ut some interesting elliptic structures arising in these algebras. In particular, we show that the screening currents satisfy elliptic analo gues of the Drinfeld relations in U-q((n) over cap).