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arXiv · 1509.03803

Refined dual stable Grothendieck polynomials and generalized Bender-Knuth involutions

Pavel Galashin·Darij Grinberg·Gaku Liu
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Abstract

The dual stable Grothendieck polynomials are a deformation of the Schur functions, originating in the study of the K-theory of the Grassmannian. We generalize these polynomials by introducing a countable family of additional parameters, and we prove that this generalization still defines symmetric functions. For this fact, we give two self-contained proofs, one of which constructs a family of involutions on the set of reverse plane partitions generalizing the Bender-Knuth involutions on semistandard tableaux, whereas the other classifies the structure of reverse plane partitions with entries 1 and 2.

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Pavel Galashin, Darij Grinberg, Gaku Liu. 2015-10-14. Refined dual stable Grothendieck polynomials and generalized Bender-Knuth involutions. https://doi.org/10.37236/5737

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