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\author{Jeffrey Kuan}
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\title{Orthogonal Polynomials}
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\begin{abstract}
The Yang--Baxter equation is cool.
\end{abstract}
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%\part{Introduction}
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Accessibility statement: \href{https://ximera.osu.edu/firststeps24html/aFirstStepInXimera/basics/Orth_Poly_WCAG}{A WCAG2.1AA compliant version of these notes} will eventually be available, once I finish writing them.
You can also \href{https://ximera.osu.edu/firststeps24html/aFirstStepInXimera/basics/Orth_Poly.tex}{download the TeX source file.}
\section{About this webpage}
These lecture notes were created with \href{https://ximera.osu.edu/}{Ximera}, an
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Funding was provided by \href{https://www.lms.ac.uk/grants/visits-uk-scheme-2}{The London Mathematical Society} and
Lancaster University, University of Bristol, University of Edinburgh, Warwick University, Queen Mary University of London, and Ximera.
\section{Orthogonal Polynomial Weights}
We have previously said that vertex weights are duality functions,
and that vertex weights are often orthogonal polynomials. Here,
we explain how this can be shown with fusion.
First, we recall some background on \(q\)--hypergeometric series.
We state a theorem
from \cite{KMMO16} and \cite{Pov13} and \cite{Man14}:
\begin{theorem}
The follow weights satisfy the Yang--Baxter equation:
\end{theorem}
\begin{thebibliography}{10}
\bibitem{KMMO16} A. Kuniba, V.V. Mangazeev, S. Maruyama, M. Okado,
Stochastic R matrix for \(U_q(A_n^{(1)})\),
Nuclear Physics B,
Volume 913,
2016,
Pages 248-277.
\bibitem{Man14} Vladimir V. Mangazeev,
On the Yang–Baxter equation for the six-vertex model,
Nuclear Physics B,
Volume 882, May 2014, Pages 70-96
\bibitem{Pov13} A.M. Povolotsky,
On the integrability of zero-range chipping models with factorized steady states
J. Phys. A, Math. Theor., 46 (2013), p. 465205
\end{thebibliography}
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