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

On Quiver W-algebras and Defects from Gauge Origami