Séminaire Lotharingien de Combinatoire, 85B.23 (2021), 12 pp.
Kohhei Motegi and Travis Scrimshaw
Refined Dual Grothendieck Polynomials, Integrability, and the Schur Measure
Abstract.
We prove a Jacobi-Trudi formula, a Littlewood identity, a Cauchy identity, and symmetries for refined dual Grothendieck polynomials by using the Lindström-Gessel-Viennot lemma and an interpretation as integrable vertex models.
We give an alternative definition of refined dual Grothendieck polynomials from the last passage percolation model.
We then prove a Jacobi-Trudi formula for skew shapes and give a new proof of a relation with the Schur measure due to Baik and Rains.
Received: December 1, 2020.
Accepted: March 1, 2021.
Final version: April 29, 2021.
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