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Free-fermions and skew stable Grothendieck polynomials

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Abstract

We present a free-fermionic presentation of the skew (dual) stable Grothendieck polynomials. A direct proof of their determinantal formulas is given from this presentation. We also introduce a combinatorial method to describe the multiplication map and its adjoint over the space of skew (dual) stable Grothendieck polynomials. This calculation requires the use of noncommutative supersymmetric Schur functions.

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Notes

  1. The k is equipped with the discrete topology.

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Acknowledgements

This work is partially supported by JSPS Kakenhi Grant Number 19K03605. The author is grateful to Professor Takeshi Ikeda for his comments on the manuscript and for his suggestions for future research.

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  1. Department of Mathematics, Tokai University, 4-1-1, Kitakaname, Hiratsuka, Kanagawa, 259-1292, Japan

    Shinsuke Iwao

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  1. Shinsuke Iwao
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Correspondence to Shinsuke Iwao.

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Iwao, S. Free-fermions and skew stable Grothendieck polynomials. J Algebr Comb 56, 493–526 (2022). https://doi.org/10.1007/s10801-022-01121-6

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  • DOI: https://doi.org/10.1007/s10801-022-01121-6

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