Entropic inequalities for matrix elements of rotation group irreducible representations

TL;DR

This paper derives new inequalities for classical polynomials by applying entropic inequalities to the matrix elements of irreducible representations of the rotation groups SU(2) and SU(1,1), linking group theory and information theory.

Contribution

It introduces novel inequalities for Jacobi and hypergeometric functions using Shannon and Tsallis entropic inequalities, connecting group representations with classical polynomial bounds.

Findings

New inequalities for Jacobi polynomials

Inequalities for Gauss hypergeometric functions

Application of entropic inequalities to group representation matrix elements

Abstract

Using the entropic inequalities for Shannon and Tsallis entropies new inequalities for some classical polynomials are obtained. To this end, an invertible mapping for the irreducible unitary representation of groups $SU(2)$ and $SU(1,1)$ like Jacoby polynomials and Gauss' hypergeometric functions, respectively, are used.