W-Algebras via Lax Type Operators

  title={W-Algebras via Lax Type Operators},
  author={Daniele Valeri},
  journal={arXiv: Mathematical Physics},
  • 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

A slow review of the AGT correspondence

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



Shifted Yangians and finite W-algebras

On classical finite and affine W -algebras

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

Quantum reduction and representation theory of superconformal algebras

Structure of classical (finite and affine) W-algebras

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

Finite W-algebras for glN

Quantum Reduction in the Twisted Case

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

Quantum Langlands duality of representations of ${\mathcal{W}}$ -algebras

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.

Exactly soluble models of conformal quantum field theory associated with the simple Lie algebra D sub n

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

Affine Algebras, Langlands Duality and Bethe Ansatz

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