Nonsymmetric Macdonald polynomials via integrable vertex models

  title={Nonsymmetric Macdonald polynomials via integrable vertex models},
  author={Alexei Borodin and Michael Wheeler},
  journal={Transactions of the American Mathematical Society},
  • A. Borodin, M. Wheeler
  • Published 15 April 2019
  • Mathematics
  • Transactions of the American Mathematical Society
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 model and a certain rotation operation that acts on our partition functions, we show that they are eigenfunctions of the Cherednik-Dunkl operators $Y_i$ for all $1 \leq i \leq n$, and are thus equal to nonsymmetric Macdonald polynomials $E_{\mu}$. Our partition functions have the combinatorial… 

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