Drinfeld–Sokolov Reduction for Difference Operators and Deformations of -Algebras¶I. The Case of Virasoro Algebra
@article{Frenkel1998DrinfeldSokolovRF, title={Drinfeld–Sokolov Reduction for Difference Operators and Deformations of -Algebras¶I. The Case of Virasoro Algebra }, author={Edward Vladimir Frenkel and Nikolai Reshetikhin and Michael Arsen'evich Semenov-Tian-Shansky}, journal={Communications in Mathematical Physics}, year={1998}, volume={192}, pages={605-629} }
Abstract:We propose a q-difference version of the Drinfeld-Sokolov reduction scheme, which gives us q-deformations of the classical -algebras by reduction from Poisson-Lie loop groups. We consider in detail the case of SL2. The nontrivial consistency conditions fix the choice of the classical r-matrix defining the Poisson-Lie structure on the loop group LSL2, and this leads to a new elliptic classical r-matrix. The reduced Poisson algebra coincides with the deformation of the classical Virasoro…
7 Citations
Drinfeld–Sokolov Reduction for Difference
Operators and Deformations of W-Algebras¶ II. The General Semisimple Case
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Abstract:The paper is the sequel to [9]. We extend the Drinfeld--Sokolov reduction procedure to q-difference operators associated with arbitrary semisimple Lie algebras. This leads to a new elliptic…
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Abstract. We define deformations of W-algebras associated to complex semisimple Lie algebras by means of quantum Drinfeld-Sokolov reduction procedure for affine quantum groups. We also introduce…
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Abstract: We construct a discrete quantum version of the Drinfeld–Sokolov correspondence for the sine-Gordon system. The classical version of this correspondence is a birational Poisson morphism…
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In this paper we study the Poisson–Lie version of the Drinfeld– Sokolov reduction defined in [13], [23]. Using the bialgebra structure related to the new Drinfeld realization of affine quantum groups…
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Abstract:We discuss some aspects of the representation theory of the deformed Virasoro algebra $\virpq$. In particular, we give a proof of the formula for the Kac determinant and then determine the…
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We investigate the structure of the elliptic algebra Uq,p(ŝl2) introduced earlier by one of the authors. Our construction is based on a new set of generating series in the quantum affine algebra…
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The q-deformed version of the Drinfeld-Sokolov reduction is extended to the case of the algebra of 'complex size matrices'; this construction generalizes earlier results of B.Khesin and F.Malikov on…
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