Quantum -algebras and elliptic algebras
Abstract
We define a quantum MediaObjects/220_2005_BF02108819_f3.jpg -algebra associated tomathfrak{s}mathfrak{l}_N as an associative algebra depending on two parameters. For special values of the parameters, this algebra becomes the ordinary MediaObjects/220_2005_BF02108819_f4.jpg -algebra ofmathfrak{s}mathfrak{l}_N , or the q-deformed classical<Figure ID="Fig3" Float="No" Category="Standard"> MediaObjects/220_2005_BF02108819_f5.jpg </Figure>-algebra algebra ofmathfrak{s}mathfrak{l}_N . We construct free field realizations of the quantum<Figure ID="Fig4" Float="No" Category="Standard"> MediaObjects/220_2005_BF02108819_f6.jpg </Figure>-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<Figure ID="Fig5" Float="No" Category="Standard"> MediaObjects/220_2005_BF02108819_f7.jpg </Figure>.
- Publication:
-
Communications in Mathematical Physics
- Pub Date:
- July 1996
- DOI:
- 10.1007/BF02108819
- arXiv:
- arXiv:q-alg/9508009
- Bibcode:
- 1996CMaPh.178..653F
- Keywords:
-
- Mathematics - Quantum Algebra;
- High Energy Physics - Theory
- E-Print:
- 26 pages, AMSLATEX