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arXiv · 2508.05457

Structure constants of Peterson Schubert calculus

Tao Gui·Yuqi Jia·Xinkai Yu·Zhexi Zhang·Yuchen Zhu
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Abstract

We give an explicit, positive, and type-uniform formula for all equivariant structure constants of the Peterson Schubert calculus in arbitrary Lie types, using only the Cartan matrix of the corresponding root system $\Phi$. This solves an open problem originally asked by Harada--Tymoczko in type A for all Lie types. As an application, we derive a type-uniform formula for the mixed $\Phi$-Eulerian numbers.

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Tao Gui, Yuqi Jia, Xinkai Yu, Zhexi Zhang, Yuchen Zhu. 2025-08-07. Structure constants of Peterson Schubert calculus. https://arxiv.org/abs/2508.05457

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