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- W4287815552 abstract "Peterson varieties are special nilpotent Hessenberg varieties that have appeared in the study of quantum cohomology, representation theory, and combinatorics. In type $A$, the Peterson variety $Y$ is a subvariety of the complete flag variety $Fl(n; mathbb C)$, and is invariant under the action of a subgroup $Scong mathbb C^*$ of $T$, where $T$ is the standard (noncompact) torus acting on $Fl(n; mathbb C)$. Using the Peterson Schubert basis introduced by Harada and Tymoczko obtained by restricting a specific set of Schubert classes from $H_T^*(Fl(n; mathbb C))$ to $H_S^*(Y)$, we describe the product structure of the equivariant cohomology $H_{S}^*(Y)$. In particular, we show that the product is manifestly positive in an appropriate sense by providing an explicit positive combinatorial formula for its structure constants. Our method requires a new combinatorial identity of binomial coefficients that generalizes Vandermonde's identity." @default.
- W4287815552 created "2022-07-26" @default.
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- W4287815552 date "2020-04-13" @default.
- W4287815552 modified "2023-09-27" @default.
- W4287815552 title "A positive formula for type $A$ Peterson Schubert calculus" @default.
- W4287815552 doi "https://doi.org/10.48550/arxiv.2004.05959" @default.
- W4287815552 hasPublicationYear "2020" @default.
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