Multi-indexed Jacobi polynomials and Maya diagrams

Abstract

Multi-indexed Jacobi polynomials are defined by the Wronskian of four types of eigenfunctions of a deformed P\"oschl-Teller Hamiltonian. We give a correspondence between multi-indexed Jacobi polynomials and pairs of Maya diagrams, and we show that any multi-indexed Jacobi polynomial is essentially equal to some multi-indexed Jacobi polynomial of two types of eigenfunction. As an application, we show a Wronskian-type formula of some special eigenstates of the deformed P\"oschl-Teller Hamiltonian.