## 3 Citations

### Drinfeld–Sokolov reduction for quantum groups and deformations of W-algebras

- Mathematics
- 2001

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…

### Discrete Quantum Drinfeld–Sokolov Correspondence

- Mathematics
- 2002

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…

### Localization of quantum biequivariant Ɗ‐modules and q–W algebras

- Mathematics
- 2012

We present a biequivariant version of Kremnizer–Tanisaki localization theorem for quantum D ‐modules. We also obtain an equivalence between a category of finitely generated equivariant modules over a…

### Discrete Miura Opers and Solutions of the Bethe Ansatz Equations

- Mathematics
- 2004

Solutions of the Bethe ansatz equations associated to the XXX model of a simple Lie algebra come in families called the populations. We prove that a population is isomorphic to the flag variety of…

### Poisson Geometry of Parabolic Bundles on Elliptic Curves

- Mathematics
- 2006

The moduli space of G-bundles on an elliptic curve with additional flag structure admits a Poisson structure. The bivector can be defined using double loop group, loop group and sheaf cohomology…

### POISSON GEOMETRY OF PARABOLIC BUNDLES ON ELLIPTIC CURVES

- Mathematics
- 2006

The moduli space of G-bundles on an elliptic curve with additional flag structure admits a Poisson structure. The bivector can be defined using double loop group, loop group and sheaf cohomology…

## References

SHOWING 1-10 OF 30 REFERENCES

### Drinfeld–Sokolov Reduction for Difference Operators and Deformations of -Algebras¶I. The Case of Virasoro Algebra

- Mathematics
- 1998

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…

### The Whittaker model of the center of the quantum group and Hecke algebras

- Mathematics
- 1999

Sevostyanov, A. 1999. The Whittaker model of the center of the quantum group and Hecke algebras. 77 pp. Uppsala. ISBN 91-506-1342-1. In 1978 Kostant suggested the Whittaker model of the center of the…

### Drinfeld–Sokolov Reduction for Difference Operators and Deformations of W-Algebras¶ II. The General Semisimple Case

- Mathematics
- 1998

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…

### Lie-Poisson structure on some Poisson Lie groups

- Mathematics
- 1992

Poisson Lie groups appeared in the work of Drinfel'd (see, e.g., [Drl, Dr2]) as classical objects corresponding to quantum groups. Going in the other direction, we may say that a Poisson Lie group is…

### Quantum Groups

- Mathematics
- 1993

This thesis consists of four papers. In the first paper we present methods and explicit formulas for describing simple weight modules over twisted generalized Weyl algebras. Under certain conditions…

### Reduction of Quantum Systems with Arbitrary First Class Constraints and Hecke Algebras

- Mathematics
- 1999

Abstract:We propose a method for reduction of quantum systems with arbitrary first-class constraints. An appropriate mathematical setting for the problem is the homology of associative algebras. For…

### Poisson Lie Groups, Quantum Duality Principle, and the Quantum Double

- Mathematics, Physics
- 1993

The Heisenberg double of a Hopf algebra may be regarded as a quantum analogue of the cotangent bundle of a Lie group. Quantum duality principle describes relations between a Hopf algebra, its dual,…

### Momentum Mappings And Reduction of Poisson Actions

- Mathematics
- 1991

An action σ: G × P→P of a Poisson Lie group G on a Poisson manifold P is called a Poisson action if σ is a Poisson map. It is believed that Poisson actions should be used to understand the “hidden…

### Regular Nilpotent Elements and Quantum Groups

- Mathematics
- 1998

Abstract:We suggest new realizations of quantum groups Uq(?) corresponding to complex simple Lie algebras, and of affine quantum groups. These new realizations are labeled by Coxeter elements of the…