Daisuke Sagaki, University of Tsukuba

Title: Toward a Pieri rule for double quantum Grothendieck polynomials

Abstract: In a joint work with Satoshi Naito (arXiv:2211.01578), we proved a Pieri rule (conjectured by Lenart and Maeno) for quantum Grothendieck polynomials, which describes the product of the quantum Grothendieck polynomial associated to a cyclic permutation and an arbitrary quantum Grothendieck polynomial as a \(\mathbb{Z}[Q_1,Q_2,\dots]\)-linear combination of quantum Grothendieck polynomials. Recently, in a joint work with Satoshi Naito and Duc-Khanh Nguyen, we are trying to extend this result to the case of double quantum Grothendieck polynomials. In this talk, I'd like to report on the progress of the joint work.