Orthogonal polynomials and the deformed Jordan plane
Abstract
We consider the unital associative algebra A with two generators X, Z obeying the defining relation [Z,X]=Z2+. We construct irreducible tridiagonal representations of A. Depending on the value of the parameter , these representations are associated to the Jacobi matrices of the para-Krawtchouk, continuous Hahn, Hahn or Jacobi polynomials.
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