Discriminants and Quasi-symmetry

TL;DR

This paper provides a geometric interpretation of quasi-symmetric representations, showing their discriminant loci form hyperplane arrangements and linking these to recent work by Halpern-Leistner and Sam.

Contribution

It introduces a geometric perspective on quasi-symmetric representations and identifies their discriminant loci as hyperplane arrangements, connecting to recent research.

Findings

Discriminant locus is a hyperplane arrangement.

Hyperplane arrangement is identified up to a shift.

Connection to recent work of Halpern-Leistner--Sam.

Abstract

This paper gives a geometric interpretation of the notion of quasi-symmetric representation and uses this to show that the discriminant locus associated to such a representation is a hyperplane arrangement. Moreover, we identify this hyperplane arrangement, up to a shift, with the one appearing in recent work of Halpern-Leistner--Sam