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} }
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.
One Citation
A slow review of the AGT correspondence
- Mathematics
- 2020
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
On classical finite and affine W -algebras
- Mathematics
- 2014
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…
Structure of classical (finite and affine) W-algebras
- 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…
Quantum Reduction in the Twisted Case
- 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…
REPRESENTATION THEORY OF W-ALGEBRAS AND HIGGS BRANCH CONJECTURE
- MathematicsProceedings 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
- MathematicsCompositio 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.
Exactly soluble models of conformal quantum field theory associated with the simple Lie algebra D sub n
- 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…
Affine Algebras, Langlands Duality and Bethe Ansatz
- Mathematics
- 1995
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…