Abstract
We continue the study of the quantization of supersymmetric integrable KdV hierarchies. We consider the N=2 KdV model based on the sl(1)(2|1) affine algebra but with a new algebraic construction for the L-operator, different from the standard Drinfeld-Sokolov reduction. We construct the quantum monodromy matrix satisfying a special version of the reflection equation and show that in the classical limit, this object precisely gives the monodromy matrix of the N=2 supersymmetric KdV system. We also show that at both the classical and the quantum levels, the trace of the monodromy matrix (transfer matrix) is invariant under two supersymmetry transformations and the zero mode of the associated U(1) current.
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 147, No. 2, pp. 303–314, May, 2006.
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Zeitlin, A.M. Quantization of the N=2 supersymmetriC KdV hierarchy. Theor Math Phys 147, 698–708 (2006). https://doi.org/10.1007/s11232-006-0071-z
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DOI: https://doi.org/10.1007/s11232-006-0071-z