# W-Algebras via Lax Type Operators

@article{Valeri2020WAlgebrasVL,
title={W-Algebras via Lax Type Operators},
author={Daniele Valeri},
journal={arXiv: Mathematical Physics},
year={2020},
pages={181-198}
}
• Daniele Valeri
• Published 16 January 2020
• Mathematics
• arXiv: Mathematical Physics
W-algebras are certain algebraic structures associated to a finite-dimensional Lie algebra Open image in new window and a nilpotent element f via Hamiltonian reduction. In this note we give a review of a recent approach to the study of (classical affine and quantum finite) W-algebras based on the notion of Lax type operators.
1 Citations
Starting with a gentle approach to the AGT correspondence from its 6d origin, these notes provide a wide survey of the literature on numerous extensions of the correspondence. This is the writeup of

## References

SHOWING 1-10 OF 53 REFERENCES

This paper is meant to be a short review and summary of recent results on the structure of finite and affine classical W-algebras, and the application of the latter to the theory of generalized
• Mathematics
• 2014
First, we derive an explicit formula for the Poisson bracket of the classical finite W-algebra Wfin(g, f ), the algebra of polynomial functions on the Slodowy slice associated to a simple Lie
• Mathematics, Physics
• 2005
We study the quantum Hamiltonian reduction for affine superalgebras in the twisted case. This leads to a general representation theory of all superconformal algebras, including the twisted ones (like
• T. Arakawa
• Mathematics
Proceedings of the International Congress of Mathematicians (ICM 2018)
• 2019
We survey a number of results regarding the representation theory of $W$-algebras and their connection with the resent development of the four dimensional $N=2$ superconformal field theories in
• Mathematics
Compositio Mathematica
• 2019
We prove duality isomorphisms of certain representations of ${\mathcal{W}}$ -algebras which play an essential role in the quantum geometric Langlands program and some related results.
• Mathematics, Physics
• 1989
We construct a class of exactly soluble models of two-dimensional conformal quantum field theory, which describes certain critical points of RSOS statistical systems, associated with the {ital D}{sub
We review various aspects of representation theory of affine algebras at the critical level, geometric Langlands correspondence, and Bethe ansatz in the Gaudin models. Geometric Langlands