Abstract
We define a quantum
-algebra associated to\(\mathfrak{s}\mathfrak{l}_N \) as an associative algebra depending on two parameters. For special values of the parameters, this algebra becomes the ordinary
-algebra of\(\mathfrak{s}\mathfrak{l}_N \), or theq-deformed classical
-algebra algebra of\(\mathfrak{s}\mathfrak{l}_N \). We construct free field realizations of the quantum
-algebra 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
.
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Communicated by G. Felder
The research of the second author was partially supported by NSF grant DMS-9501414.
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Feigin, B., Frenkel, E. Quantum
-algebras and elliptic algebras.
Commun.Math. Phys. 178, 653–677 (1996). https://doi.org/10.1007/BF02108819
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DOI: https://doi.org/10.1007/BF02108819