Refined dual Grothendieck polynomials, integrability, and the Schur measure.(English)Zbl 1505.05134
Summary: 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 toJ. Baik andE. M. Rains [Duke Math. J. 109, No. 1, 1–65 (2001;Zbl 1007.05096)].
MSC:
| 05E05 | Symmetric functions and generalizations |
Citations:
Zbl 1007.05096Software:
SageMathCite
References:
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