Recurrence Relations of the Multi-Indexed Orthogonal Polynomials IV :   closure relations and creation/annihilation operators
  We consider the exactly solvable quantum mechanical systems whose eigenfunctions are described by the multi-indexed orthogonal polynomials of Laguerre, Jacobi, Wilson and Askey-Wilson types. Corresponding to the recurrence relations with constant coefficients for the $M$-indexed orthogonal polynomials, it is expected that the systems satisfy the generalized closure relations. In fact we can verify this statement for small $M$ examples. The generalized closure relation gives the exact Heisenberg operator solution of a certain operator, from which the creation and annihilation operators of the system are obtained. 
Satoru Odake
math-ph hep-th math.CA math.MP nlin.SI