Abstract
The factorial flagged Grothendieck polynomials are defined by flagged set-valued tableaux of Knutson–Miller–Yong [10]. We show that they can be expressed by a Jacobi–Trudi type determinant formula, generalizing the work of Hudson–Matsumura [8]. As an application, we obtain alternative proofs of the tableau and the determinant formulas of vexillary double Grothendieck polynomials, which were originally obtained by Knutson–Miller–Yong [10] and Hudson–Matsumura [8] respectively. Furthermore, we show that each factorial flagged Grothendieck polynomial can be obtained by applying K-theoretic divided difference operators to a product of linear polynomials.
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Acknowledgements
We would like to thank the anonymous referees, whose observations and suggestions significantly enhanced the presentation. The first author is supported by Grant-in-Aid for Young Scientists (B) 16K17584.
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Matsumura, T., Sugimoto, S. (2020). Factorial Flagged Grothendieck Polynomials. In: Hu, J., Li, C., Mihalcea, L.C. (eds) Schubert Calculus and Its Applications in Combinatorics and Representation Theory. ICTSC 2017. Springer Proceedings in Mathematics & Statistics, vol 332. Springer, Singapore. https://doi.org/10.1007/978-981-15-7451-1_1
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