Title: New Determinant Expressions of the Multi-indexed Orthogonal Polynomials in Discrete Quantum Mechanics,
Abstract: The multi-indexed orthogonal polynomials (the Meixner, little $q$-Jacobi
(Laguerre), ($q$-)Racah, Wilson, Askey-Wilson types) satisfying second order
difference equations were constructed in discrete quantum mechanics. They are
polynomials in the sinusoidal coordinates $\eta(x)$ ($x$ is the coordinate of
quantum system) and expressed in terms of the Casorati determinants whose
matrix elements are functions of $x$ at various points. By using shape
invariance properties, we derive various equivalent determinant expressions,
especially those whose matrix elements are functions of the same point $x$.
Except for the ($q$-)Racah case, they can be expressed in terms of $\eta$ only,
without explicit $x$-dependence.