• Refined dual Grothendieck poly...

Result: Refined dual Grothendieck polynomials, integrability, and the Schur measure

Title:
Refined dual Grothendieck polynomials, integrability, and the Schur measure
Authors:
Motegi, Kohei, Scrimshaw, Travis
Source:
Selecta Mathematica. 31
Publication Status:
Preprint
Publisher Information:
Springer Science and Business Media LLC, 2025.
Publication Year:
2025
Subject Terms:
vertex model, 05E05, 82B23, 14M15, 05A19, 60B20, Symmetric functions and generalizations, Classical problems, Schubert calculus, Probability (math.PR), K-Theory and Homology (math.KT), Grassmannians, Schubert varieties, flag manifolds, 01 natural sciences, Random matrices (probabilistic aspects), Mathematics - K-Theory and Homology, Mathematics - Quantum Algebra, dual Grothendieck polynomial, FOS: Mathematics, Mathematics - Combinatorics, Quantum Algebra (math.QA), Combinatorics (math.CO), 0101 mathematics, Exactly solvable models, Bethe ansatz, last passage percolation, Mathematics - Probability, Combinatorial identities, bijective combinatorics
Document Type:
Academic journal Article
File Description:
application/xml
Language:
English
ISSN:
1420-9020
1022-1824
DOI:
10.1007/s00029-025-01041-w
DOI:
10.48550/arxiv.2012.15011
Access URL:
http://arxiv.org/abs/2012.15011
https://zbmath.org/8032686
https://doi.org/10.1007/s00029-025-01041-w
Rights:
Springer Nature TDM
arXiv Non-Exclusive Distribution
Accession Number:
edsair.doi.dedup.....b885b07c6615e408c21eb4c2d7e8c3f2
Database:
OpenAIRE

Further Information

We construct a vertex model whose partition function is a refined dual Grothendieck polynomial, where the states are interpreted as nonintersecting lattice paths. Using this, we show refined dual Grothendieck polynomials are multi-Schur functions and give a number of identities, including a Littlewood and Cauchy(-Littlewood) identity. We then refine Yeliussizov's connection between dual Grothendieck polynomials and the last passage percolation (LPP) stochastic process discussed by Johansson. By refining algebraic techniques of Johansson, we show Jacobi-Trudi formulas for skew refined dual Grothendieck polynomials conjectured by Grinberg and recover a relation between LPP and the Schur process due to Baik and Rains. Lastly, we extend our vertex model techniques to show some identities for refined Grothendieck polynomials, including a Jacobi-Trudi formula.
55 pages, 5 tables