Algebraically Independent Generators for the Algebra of Invariant Differential Operators on $\mathrm{SL}_n(\mathbb R)/\mathrm{SO}_n(\mathbb R)$

TL;DR

This paper explicitly constructs algebraically independent generators for the algebra of invariant differential operators on the symmetric space related to SL_n(R), advancing understanding of its algebraic structure.

Contribution

It provides a new explicit set of generators for the algebra of invariant differential operators on SL_n(R)/SO_n(R), which was previously not known.

Findings

Explicit algebraically independent generators constructed

Enhanced understanding of the algebraic structure of invariant differential operators

Potential applications in harmonic analysis and representation theory

Abstract

We provide an explicit set of algebraically independent generators for the algebra of invariant differential operators on the Riemannian symmetric space associated with $\SL_n(\R)$.