The Racah algebra and $\mathfrak{sl}_n$

TL;DR

This paper conjectures an embedding of the Racah algebra into the universal enveloping algebra of rak{sl}_n, supported by differential operator realizations and explicit embeddings.

Contribution

It introduces a conjecture about embedding the Racah algebra into rak{sl}_n's universal enveloping algebra with concrete realizations as differential operators.

Findings

Evidence provided through differential operator realizations

Explicit embedding constructed in the differential operator framework

Supports the conjecture of algebraic embedding

Abstract

We conjecture the existence of an embedding of the Racah algebra into the universal enveloping algebra of $\mathfrak{sl}_n$. Evidence of this conjecture is offered by realizing both algebras using differential operators and giving an embedding in this realization.