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Geometry of Peterson Schubert calculus in type A and left-right diagrams

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arxiv 2104.02914 v2 pith:4QIIEGWP submitted 2021-04-07 math.AG math.CO

Hiraku Abe , Tatsuya Horiguchi , Hideya Kuwata , Haozhi Zeng This is my paper · ORCID
classification math.AGmath.CO
keywords basispetersonadditivegeometryvarietycalculuscertaincohomology
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We introduce an additive basis of the integral cohomology ring of the Peterson variety which reflects the geometry of certain subvarieties of the Peterson variety. We explain the positivity of the structure constants from a geometric viewpoint, and provide a manifestly positive combinatorial formula for them. We also prove that our basis coincides with the additive basis introduced by Harada-Tymoczko.

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  1. Mixed Eulerian numbers and beyond

    math.AG 2025-02 accept novelty 8.0 of 10

    First explicit formula for mixed Eulerian numbers, and proof that matroidal mixed Eulerian numbers determine Derksen's G-invariant.

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