Factorial Flagged Grothendieck Polynomials

Tomoo Matsumura; Shogo Sugimoto

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arXiv · 1903.02169

Factorial Flagged Grothendieck Polynomials

Tomoo Matsumura·Shogo Sugimoto

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Abstract

We show that the factorial flagged Grothendieck polynomials defined by flagged set-valued tableaux of Knutson-Miller-Yong can be expressed by a Jacobi-Trudi type determinant formula, generalizing the work of Hudson-Matsumura. In particular, we obtain an alternative proof of the tableau and determinant formulas of vexillary double Grothendieck polynomials, that have been obtained by Knutson-Miller-Yong and Hudson-Matsumura respectively. Moreover, we show that each factorial flagged Grothendieck polynomial can be obtained from a product of linear polynomials by applying K-theoretic divided difference operators.

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Tomoo Matsumura, Shogo Sugimoto. 2019-03-06. Factorial Flagged Grothendieck Polynomials. https://arxiv.org/abs/1903.02169

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