# On Quiver W-algebras and Defects from Gauge Origami

## TL;DR

This paper explores the connections between gauge origami, quiver W-algebras, and the AGT duality, demonstrating exact parameter matchings and relating algebraic structures to instanton partition functions in a large-n limit.

## Contribution

It introduces a framework to study dualities using gauge origami, linking quiver W-algebras to affine Hecke algebras and instanton partition functions.

## Key findings

- Exact matchings between parameters of dual theories
- Relation of quiver W-algebras to affine Hecke algebras
- Representation of modules via instanton partition functions

## Abstract

In this note, using Nekrasov's gauge origami framework, we study two different versions of the the BPS/CFT correspondence - first, the standard AGT duality and, second, the quiver W algebra construction which has been developed recently by Kimura and Pestun. The gauge origami enables us to work with both dualities simultaneously and find exact matchings between the parameters. In our main example of an A-type quiver gauge theory, we show that the corresponding quiver qW-algebra and its representations are closely related to a large-n limit of spherical gl(n) double affine Hecke algebra whose modules are described by instanton partition functions of a defect quiver theory.