Notes on parameters of quiver Hecke algebras

TL;DR

This paper extends the correspondence between simple modules over quiver Hecke algebras and the upper global basis to the case of generic parameters in symmetric generalized Cartan matrices, building on prior work with special parameters.

Contribution

It demonstrates that the correspondence holds for generic parameters, not just special ones, in symmetric generalized Cartan matrix cases.

Findings

Simple modules with generic parameters correspond to the upper global basis.

The result generalizes previous work from special to generic parameters.

Supports the robustness of the basis-module correspondence in quiver Hecke algebras.

Abstract

Varagnolo-Vasserot and Rouquier proved that, in a symmetric generalized Cartan matrix case, the simple modules over the quiver Hecke algebra with a special parameter correspond to the upper global basis. In this note we show that the simple modules over the quiver Hecke algebras with a generic parameter also correspond to the upper global basis in a symmetric generalized Cartan matrix case.