The integral cohomology rings of Peterson varieties in type A

Abstract

In this paper, we study the ring structure of the integral cohomology of the Peterson variety of type ${\text{A}}_{n-1}$. We give two kinds of descriptions: (1) we show that it is isomorphic to the ${\mathfrak{S}}_n$-invariant subring of the integral cohomology ring of the permutohedral variety, (2) we determine the ring structure in terms of ring generators and their relations.

32 pages