Stratifying KLR algebras of affine ADE types

TL;DR

This paper extends the theory of KLR algebras of affine ADE types by generalizing imaginary Howe duality to arbitrary convex preorders and proves their proper stratification under certain conditions.

Contribution

It introduces a generalization of imaginary Howe duality for KLR algebras of affine ADE types to arbitrary convex preorders and establishes their proper stratification.

Findings

KLR algebras are properly stratified under specific conditions

Generalization of imaginary Howe duality to broader preorders

Explicit bounds on the characteristic of the ground field

Abstract

We generalize imaginary Howe duality for KLR algebras of affine ADE types, developed in our previous paper, from balanced to arbitrary convex preorders. Under the assumption that the characteristic of the ground field is greater than some explicit bound, we prove that these KLR algebras are properly stratified.