English

The q-AGT-W relations via shuffle algebras

Representation Theory 2017-11-28 v4 High Energy Physics - Theory Mathematical Physics Algebraic Geometry math.MP

Abstract

We construct the action of the q-deformed W-algebra on its level r representation geometrically, using the moduli space of U(r) instantons on the plane and the double shuffle algebra. We give an explicit LDU decomposition for the action of W-algebra currents in the fixed point basis of the level r representation, and prove a relation between the Carlsson-Okounkov Ext operator and intertwiners for the deformed W-algebra. We interpret this result as a q-deformed version of the AGT-W relations.

Keywords

Cite

@article{arxiv.1608.08613,
  title  = {The q-AGT-W relations via shuffle algebras},
  author = {Andrei Neguţ},
  journal= {arXiv preprint arXiv:1608.08613},
  year   = {2017}
}