Quantum W-algebras and Elliptic Algebras

Details Quantum W-algebras and Elliptic Algebras Quantum W-algebras and Elliptic Algebras

1995-08-17

arxiv.org/abs/q-alg/9508009v1

Commun.Math.Phys. 178 (1996) 653-678

Physics

High Energy Physics

High Energy Physics - Theory

26 pages, AMSLATEX

Scientific paper

10.1007/BF02108819

We define quantum W-algebras generalizing the results of Reshetikhin and the second author, and Shiraishi-Kubo-Awata-Odake. The quantum W-algebra associated to sl_N is an associative algebra depending on two parameters. For special values of parameters it becomes the ordinary W-algebra of sl_N, or the q-deformed classical W-algebra of sl_N. We construct free field realizations of the quantum W-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 U_q(n^).

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