The Orlik-Terao Algebra and the Cohomology of Configuration Space

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.

KEYWORDS:

• symmetric group
• configuration space
• hyperplane arrangement

2000 AMS SUBJECT CLASSIFICATION:

• 14N20
• 55R80
• 20C30
• 55N33

Acknowledgments

The authors are grateful to Nick Addington, Richard Stanley, Dan Petersen, and Ben Webster for their valuable suggestions and conversations. All computations were performed with the assistance of the computer algebra systems SAGE [Stein et al. 15] and Macaulay 2 [Grayson and Stillman 00].

Funding

Nicholas Proudfoot was supported by the NSF grant DMS-0950383.