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Communication Dans Un Congrès Discrete Mathematics and Theoretical Computer Science Année : 2020

A dual approach to structure constants for K-theory of Grassmannians

Résumé

The problem of computing products of Schubert classes in the cohomology ring can be formulated as theproblem of expanding skew Schur polynomial into the basis of ordinary Schur polynomials. We reformulate theproblem of computing the structure constants of the Grothendieck ring of a Grassmannian variety with respect to itsbasis of Schubert structure sheaves in a similar way; we address the problem of expanding the generating functions forskew reverse-plane partitions into the basis of polynomials which are Hall-dual to stable Grothendieck polynomials. From this point of view, we produce a chain of bijections leading to Buch’s K-theoretic Littlewood-Richardson rule.
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Dates et versions

hal-02168126 , version 1 (28-06-2019)

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Huilan Li, Jennifer Morse, Pat Shields. A dual approach to structure constants for K-theory of Grassmannians. 28-th International Conference on Formal Power Series and Algebraic Combinatorics, Simon Fraser University, Jul 2016, Vancouver, Canada. ⟨10.46298/dmtcs.6361⟩. ⟨hal-02168126⟩
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