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A Murnaghan–Nakayama Rule for Grothendieck Polynomials of Grassmannian Type

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Abstract

We consider the Grothendieck polynomials appearing in the K-theory of Grassmannians, which are analogs of Schur polynomials. This paper aims to establish a version of the Murnaghan–Nakayama rule for Grothendieck polynomials of the Grassmannian type. This rule allows us to express the product of a Grothendieck polynomial with a power-sum symmetric polynomial into a linear combination of other Grothendieck polynomials.

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Acknowledgements

This work is supported by the Ministry of Education and Training, Vietnam, under project code B2022-CTT-02: “Study some combinatorial models in Representation Theory”, 2022-2023 (Decision No.1323/QD-BGDDT, May 19, 2022). Khanh would like to express his sincere gratitude for the Visiting Fellowship supported by MathCoRe and Prof. Petra Schwer at Otto-von-Guericke-Universität Magdeburg. He would also like to thank Prof. Cristian Lenart for his strong encouragement and for taking his time to read the manuscript and give valuable comments. Hiep would like to thank Prof. Takeshi Ikeda for introducing Grothendieck polynomials and explaining their importance in the study of K-theory of Grassmannians. Thuy was partially supported by the Vietnam Academy of Science and Technology under grant number DLTE00.04/23-24.

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Authors and Affiliations

  1. Institut für Algebra und Geometrie, Otto-von-Guericke-Universität, Magdeburg, Germany

    Duc-Khanh Nguyen

  2. Faculty of Mathematics and Computer Science, University of Da Lat, 1 Phu Dong Thien Vuong, Da Lat City, Lam Dong, Vietnam

    Dang Tuan Hiep

  3. Decentralized Applied Crypto Laboratory, University of Science, VNU-HCMC, Ho Chi Minh City, Vietnam

    Tran Ha Son

  4. Institute of Mathematics, Vietnam Academy of Science and Technology, 18 Hoang Quoc Viet Road, Cau Giay District, Hanoi, Vietnam

    Do Le Hai Thuy

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  1. Duc-Khanh Nguyen
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  2. Dang Tuan Hiep
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  3. Tran Ha Son
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  4. Do Le Hai Thuy
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Correspondence to Duc-Khanh Nguyen.

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Communicated by Matjaž Konvalinka.

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Nguyen, DK., Hiep, D.T., Son, T.H. et al. A Murnaghan–Nakayama Rule for Grothendieck Polynomials of Grassmannian Type. Ann. Comb. 28, 155–168 (2024). https://doi.org/10.1007/s00026-023-00659-x

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