On R-matrix formulation of qq-characters

TL;DR

This paper develops an R-matrix approach to qq-characters and deformed W-algebras using DIM algebra, providing a unified framework for various types and their elliptic extensions in gauge theories.

Contribution

It introduces a novel R-matrix formulation of qq-characters based on DIM algebra, unifying different types and elliptic versions within a geometric gauge theory context.

Findings

Unified description of qq-characters of A_n type

Extension to elliptic uplifts of qq-characters

Connection between R-matrix, DIM algebra, and gauge theory representations

Abstract

We introduce an R-matrix formulation of qq-characters and corresponding Frenkel-Reshetikhin deformed W-algebras. The R-matrix featuring in the construction is of Ding-Iohara-Miki (DIM) algebra, while the type of the qq-character is determined by the network of Fock representations corresponding to a web of 5-branes geometrically engineering a quiver gauge theory. Our formulation gives a unified description of qq-characters of $A_n$ type and their elliptic uplifts.