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<p>The quadratic rank two Jacobi algebra is identified from the relations obeyed by the bispectral operators of the two-variable Jacobi polynomials orthogonal on the triangle. It is seen to admit as subalgebras Racah and Jacobi algebras of rank one. The dual realizations in terms of differential operators in the variable representation and in terms of difference operators in the degree representation are provided. Structure relations for the two-variable Jacobi polynomials are obtained as a by-product.</p>

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The Rank Two Jacobi Algebra

  • 期刊论文

  • 发表日期：

    2025年12月5日

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  • Nicolas Crampé,
  • Satoshi Tsujimoto,
  • Luc Vinet,
  • Alexei Zhedanov

摘要

The quadratic rank two Jacobi algebra is identified from the relations obeyed by the bispectral operators of the two-variable Jacobi polynomials orthogonal on the triangle. It is seen to admit as subalgebras Racah and Jacobi algebras of rank one. The dual realizations in terms of differential operators in the variable representation and in terms of difference operators in the degree representation are provided. Structure relations for the two-variable Jacobi polynomials are obtained as a by-product.