• Corpus ID: 230524035

# Colored Fermionic Vertex Models and Symmetric Functions

@inproceedings{Aggarwal2021ColoredFV,
title={Colored Fermionic Vertex Models and Symmetric Functions},
author={Amol Aggarwal and Alexei Borodin and Michael Wheeler},
year={2021}
}
• Published 5 January 2021
• Mathematics
In this text we introduce and analyze families of symmetric functions arising as partition functions for colored fermionic vertex models associated with the quantized affine Lie superalgebra Uq ( ŝl(1|n) ) . We establish various combinatorial results for these vertex models and symmetric functions, which include the following. (1) We apply the fusion procedure to the fundamental R-matrix for Uq ( ŝl(1|n) ) to obtain an explicit family of vertex weights satisfying the Yang–Baxter equation. (2…

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## References

SHOWING 1-10 OF 93 REFERENCES
Higher spin six vertex model and symmetric rational functions
• Mathematics
• 2016
We consider a fully inhomogeneous stochastic higher spin six vertex model in a quadrant. For this model we derive concise integral representations for multi-point q-moments of the height function and
Lectures on Integrable Probability: stochastic vertex models and symmetric functions
• Mathematics
• 2018
We consider a homogeneous stochastic higher spin six vertex model in a quadrant. For this model we derive concise integral representations for multi-point q-moments of the height function and for the
Coloured stochastic vertex models and their spectral theory
• Mathematics
• 2018
This work is dedicated to $\mathfrak{sl}_{n+1}$-related integrable stochastic vertex models; we call such models coloured. We prove several results about these models, which include the following:
Colored Vertex Models and Iwahori Whittaker Functions
• Mathematics
• 2019
We give a recursive method for computing all values of a basis of Whittaker functions for unramified principal series invariant under an Iwahori or parahoric subgroup of a split reductive group $G$
Vertex models, TASEP and Grothendieck polynomials
• Mathematics
• 2013
We examine the wavefunctions and their scalar products of a one-parameter family of integrable five-vertex models. At a special point of the parameter, the model investigated is related to an
Stochastic Higher Spin Vertex Models on the Line
• Mathematics
• 2015
We introduce a four-parameter family of interacting particle systems on the line, which can be diagonalized explicitly via a complete set of Bethe ansatz eigenfunctions, and which enjoy certain
Nonsymmetric Macdonald polynomials via integrable vertex models
• Mathematics
Transactions of the American Mathematical Society
• 2020
Starting from an integrable rank-$n$ vertex model, we construct an explicit family of partition functions indexed by compositions $\mu = (\mu_1,\dots,\mu_n)$. Using the Yang-Baxter algebra of the
Ribbon tableaux and the Heisenberg algebra
Abstract.In [LLT] Lascoux, Leclerc and Thibon introduced symmetric functions which are spin and weight generating functions for ribbon tableaux. This article is aimed at studying these functions in