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arXiv · 2111.15663

Equivariant Chevalley, Giambelli, and Monk Formulae for the Peterson Variety

Rebecca Goldin·Rahul Singh
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Abstract

We present a formula for the Poincaré dual in the flag manifold of the equivariant fundamental class of any regular nilpotent or regular semisimple Hessenberg variety as a polynomial in terms of certain Chern classes. We then develop a type-independent proof of the Giambelli formula for the Peterson variety, and use this formula to compute the intersection multiplicity of a Peterson variety with an opposite Schubert variety corresponding to a Coxeter word. Finally, we develop an equivariant Chevalley formula for the cap product of a divisor class with a fundamental class, and a dual Monk rule, for the Peterson variety.

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Rebecca Goldin, Rahul Singh. 2026-01-06. Equivariant Chevalley, Giambelli, and Monk Formulae for the Peterson Variety. https://arxiv.org/abs/2111.15663

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