The Orlik-Terao algebra and the cohomology of configuration space

TL;DR

This paper develops a recursive algorithm for the Orlik-Terao algebra of type A_{n-1} Coxeter arrangements and conjectures a connection to the cohomology of configuration spaces in SU(2).

Contribution

It introduces a recursive method for computing the Orlik-Terao algebra as an S_n representation and proposes a conjecture linking it to configuration space cohomology.

Findings

Recursive algorithm for Orlik-Terao algebra of type A_{n-1}

Conjectural link between algebra representation and configuration space cohomology

Extension of conjecture to general graphical arrangements

Abstract

We give a recursive algorithm for computing the Orlik-Terao algebra of the Coxeter arrangement of type A_{n-1} as a graded representation of S_n, and we give a conjectural description of this representation in terms of the cohomology of the configuration space of n points in SU(2) modulo translation. We also give a version of this conjecture for more general graphical arrangements.