Shuffle algebras for quivers and R-matrices

TL;DR

This paper introduces slope subalgebras within shuffle algebras linked to doubled quivers, providing a factorization of the universal R-matrix and proposing a conjecture relating it to Nakajima quiver varieties.

Contribution

It defines new slope subalgebras in shuffle algebras and conjectures their R-matrix factorization aligns with existing geometric constructions.

Findings

Proposed a new factorization of the universal R-matrix.

Conjectured equivalence with Nakajima quiver variety-based factorization.

Abstract

We define slope subalgebras in the shuffle algebra associated to a (doubled) quiver, thus yielding a factorization of the universal R-matrix of the double of the shuffle algebra in question. We conjecture that this factorization matches the one defined by [1, 18, 32, 33, 34] using Nakajima quiver varieties.