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arXiv · 2203.02629

The integral cohomology rings of Peterson varieties in type A

Hiraku Abe·Haozhi Zeng
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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.

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Hiraku Abe, Haozhi Zeng. 2022-03-05. The integral cohomology rings of Peterson varieties in type A. https://arxiv.org/abs/2203.02629

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