Affinizations and R-matrices for quiver Hecke algebras

TL;DR

This paper introduces affinizations and R-matrices for general quiver Hecke algebras, extending known properties from symmetric cases, and constructs tensor functors between their module categories using duality data.

Contribution

It generalizes the concepts of affinizations and R-matrices to all quiver Hecke algebras and develops a framework for tensor functors via duality data.

Findings

Affinizations and R-matrices have similar properties in general quiver Hecke algebras as in symmetric cases.

Constructed tensor functors between graded module categories of different quiver Hecke algebras.

Provided examples illustrating the application of the duality datum and tensor functors.

Abstract

We introduce the notion of affinizations and R-matrices for arbitrary quiver Hekcke algebras. We show that they enjoy similar properties to those for symmetric quiver Hecke algebras. We next define the notion of a duality datum and construct a tensor functor between graded module categories of two quiver Hecke algebras. We give several examples of such functors .