Two linear transformations each tridiagonal with respect to an eigenbasis of the other ; an algebraic approach to the Askey scheme of orthogonal polynomials ∗

@inproceedings{Terwilliger2004TwoLT,
  title={Two linear transformations each tridiagonal with respect to an eigenbasis of the other ; an algebraic approach to the Askey scheme of orthogonal polynomials ∗},
  author={Paul Terwilliger},
  year={2004}
}
Let K denote a field, and let V denote a vector space over K with finite positive dimension. We consider a pair of linear transformations A : V → V and A : V → V that satisfy the following two conditions: (i) There exists a basis for V with respect to which the matrix representing A is irreducible tridiagonal and the matrix representing A is diagonal. (ii) There exists a basis for V with respect to which the matrix representing A is irreducible tridiagonal and the matrix representing A is… CONTINUE READING