Hidden $sl_2$-algebra of finite-difference equations

TL;DR

This paper explores the relationship between polynomial solutions of finite-difference equations and finite-dimensional representations of the $sl_2$-algebra, revealing a hidden algebraic structure.

Contribution

It establishes a novel connection between finite-difference equations and $sl_2$-algebra representations, uncovering a hidden algebraic structure.

Findings

Polynomial solutions correspond to finite-dimensional $sl_2$-representations

Revealed a hidden $sl_2$-algebra structure in finite-difference equations

Provides a new algebraic perspective on finite-difference equations

Abstract

The connection between polynomial solutions of finite-difference equations and finite-dimensional representations of the $sl_2$-algebra is established (the talk given at the Wigner Symposium, Guadalajara, Mexico, August 1995, to be published in the Proceedings)