2000 character limit reached
Orthogonal polynomials and the deformed Jordan plane (2104.13960v1)
Published 28 Apr 2021 in math.RT, math-ph, math.MP, and math.RA
Abstract: We consider the unital associative algebra $\mathcal{A}$ with two generators $\mathcal{X}$, $\mathcal{Z}$ obeying the defining relation $[\mathcal{Z},\mathcal{X}]=\mathcal{Z}2+\Delta$. We construct irreducible tridiagonal representations of $\mathcal{A}$. Depending on the value of the parameter $\Delta$, these representations are associated to the Jacobi matrices of the para-Krawtchouk, continuous Hahn, Hahn or Jacobi polynomials.
Paper Prompts
Sign up for free to create and run prompts on this paper using GPT-5.
Top Community Prompts
Collections
Sign up for free to add this paper to one or more collections.