Abstract
We study the possibility to establish L-operator's formalism by Faddeev-Reshetikhin-Takhtajan-Semenov-Tian-Shansky (FRST) for quantized current algebras, that is, for quantum affine algebras in the 'new realization' by V. Drinfeld with the corresponding Hopf algebra structure and for their Yangian counterpart. We establish this formalism using the twisting procedure by Tolstoy and the second author and explain the problems which on FRST approach encounters for quantized current algebras. We also show that, for the case of Uq(s-fraktur sign̂l-fraktur signn), entries of the L-operators of the FRTS type give the Drinfeld current operators for the nonsimple roots, which we discovered recently. As an application, we deduce the commutation relations between these current operators for Uq (s-fraktur sign̂l-fraktur sign3).
Original language | English |
---|---|
Pages (from-to) | 331-352 |
Number of pages | 22 |
Journal | Letters in Mathematical Physics |
Volume | 45 |
Issue number | 4 |
DOIs | |
Publication status | Published - Sept 1998 |
Externally published | Yes |
Keywords
- FRTS approach
- Quantized current algebras
- Quantum affine algebras