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Free fermions and canonical Grothendieck polynomials
Iwao, Shinsuke1; Motegi, Kohei2; Scrimshaw, Travis3
1 Faculty of Business and Commerce Keio University Hiyosi 4–1–1, Kohoku-ku, Yokohama-si Kanagawa 223-8521 (Japan)
2 Faculty of Marine Technology Tokyo University of Marine Science and Technology Etchujima 2–1–6, Koto-Ku Tokyo, 135-8533 (Japan)
3 Faculty of Science Hokkaido University 5 Chōme Kita 8 Jōnishi, Kita Ward Sapporo, Hokkaidō 060-0808 (Japan)
Algebraic Combinatorics, Volume 7 (2024) no. 1, pp. 245-274.

We give a presentation of refined (dual) canonical Grothendieck polynomials and their skew versions using free fermions. Using this, we derive a number of identities, including the skew Cauchy identities, branching rules, expansion formulas, and integral formulas.

Received:
Revised:
Accepted:
Published online:
DOI: 10.5802/alco.332
Classification: 05E05, 82B23, 14M15, 05A19
Keywords: Grothendieck polynomial, free fermion

Iwao, Shinsuke 1; Motegi, Kohei 2; Scrimshaw, Travis 3

1 Faculty of Business and Commerce Keio University Hiyosi 4–1–1, Kohoku-ku, Yokohama-si Kanagawa 223-8521 (Japan)
2 Faculty of Marine Technology Tokyo University of Marine Science and Technology Etchujima 2–1–6, Koto-Ku Tokyo, 135-8533 (Japan)
3 Faculty of Science Hokkaido University 5 Chōme Kita 8 Jōnishi, Kita Ward Sapporo, Hokkaidō 060-0808 (Japan)
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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Iwao, Shinsuke; Motegi, Kohei; Scrimshaw, Travis. Free fermions and canonical Grothendieck polynomials. Algebraic Combinatorics, Volume 7 (2024) no. 1, pp. 245-274. doi : 10.5802/alco.332. https://alco.centre-mersenne.org/articles/10.5802/alco.332/

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