The Frobenius characteristic of the Orlik-Terao algebra of type A. (English) Zbl 1519.52018
Summary: We provide a new virtual description of the symmetric group action on the cohomology of ordered configuration space on \(SU_2\) up to translations. We use this formula to prove the Moseley-Proudfoot-Young conjecture. As a consequence we obtain the graded Frobenius character of the Orlik-Terao algebra of type \(A_n\).
MSC:
| 52C35 | Arrangements of points, flats, hyperplanes (aspects of discrete geometry) |
| 13C40 | Linkage, complete intersections and determinantal ideals |
| 13D40 | Hilbert-Samuel and Hilbert-Kunz functions; Poincaré series |
| 13D02 | Syzygies, resolutions, complexes and commutative rings |
| 55R80 | Discriminantal varieties and configuration spaces in algebraic topology |
| 55N33 | Intersection homology and cohomology in algebraic topology |
| 20C30 | Representations of finite symmetric groups |
