Spherical Functions for the Quantum Group su_q(2)

TL;DR

This paper develops q-analogues of classical spherical functions and Legendre polynomials using the representation theory of the quantum group su_q(2), extending variable separation techniques to differential-dilation equations.

Contribution

It introduces new q-analogues of spherical functions and Legendre polynomials based on su_q(2) representation theory, expanding classical mathematical tools into the quantum group context.

Findings

Defined q-analogues of Wigner rotation matrices

Extended variable separation methods to differential-dilation equations

Provided a framework for spherical functions in quantum groups

Abstract

The representation theory of the quantum group su$_q(2)$ is used to introduce $q$-analogues of the Wigner rotation matrices, spherical functions, and Legendre polynomials. The method amounts to an extension of variable separation from Laplace equations to certain differential-dilation equations.