Canonical basis, KLR-algebras and parity sheaves

TL;DR

This paper constructs a basis for the positive part of a quantum algebra related to Dynkin quivers using parity sheaves, linking geometric and algebraic structures.

Contribution

It introduces a new basis construction for quantum groups via parity sheaves, connecting geometric methods with algebraic representations.

Findings

Established a basis for the positive part of quantum groups using parity sheaves.

Linked geometric and algebraic approaches in the context of Dynkin quivers.

Provided a new perspective on quantum algebra structures.

Abstract

We give a construction of a basis of the positive part of the Drinfeld-Jimbo quantum enveloping algebra associated with a Dynkin quiver in terms of parity sheaves.