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arXiv · 2211.01578

Pieri-type multiplication formula for quantum Grothendieck polynomials

Satoshi Naito·Daisuke Sagaki
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Abstract

The purpose of this paper is to prove a Pieri-type multiplication formula for quantum Grothendieck polynomials, which was conjectured by Lenart-Maeno. This formula would enable us to compute explicitly the quantum product of two arbitrary (opposite) Schubert classes in the (small) quantum $K$-theory ring $QK(Fl_{n})$ of the (full) flag manifold $Fl_{n}$ of type $A_{n-1}$ on the basis of the fact that quantum Grothendieck polynomials represent (opposite) Schubert classes in $QK(Fl_{n})$.

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Satoshi Naito, Daisuke Sagaki. 2022-11-03. Pieri-type multiplication formula for quantum Grothendieck polynomials. https://arxiv.org/abs/2211.01578

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