Combinatorial characterization of simple-spectrum quiver representations

Determine a combinatorial characterization of Weyl-group elements whose associated quiver representations have simple torus spectrum and whose fixed-quasimap vertex functions admit reverse-plane-partition formulas.

Background

The paper gives examples beyond dominant-minuscule, minuscule, and fully commutative Weyl-group elements for which the torus acts with simple spectrum on the tautological spaces. In these cases, fixed quasimaps are still described by reverse plane partitions on an associated colored poset.

Because none of the standard Weyl-group conditions captures precisely when this phenomenon occurs, the authors explicitly pose the problem of finding the correct combinatorial criterion.