Horn inequalities on a quiver with an involution

TL;DR

This paper provides an inductive description of the cone of semi-invariants for quivers, with a focus on anti-invariant weights in quivers with involution, refining existing inequalities.

Contribution

It introduces a new inductive approach to describe semi-invariant cones and refines inequalities for anti-invariant weights in involutive quivers.

Findings

Inductive description of semi-invariant cones

Refined inequalities for anti-invariant weights

Application to quivers with involution

Abstract

Derksen and Weyman described the cone of semi-invariants associated with a quiver. We give an inductive description of this cone, followed by an example of refinement of the inequalities characterising anti-invariant weights in the case of a quiver equipped with an involution.