In his 1974 paper, Gelbart developed a theory of Stiefel Harmonics for the space $\operatorname{SO}(n,\mathbb{R})/\operatorname{SO}(n-m,\mathbb{R})$ generalizing the classical theory of spherical harmonics. (Provided that $n\geq 2m$). In this talk we will discuss a new approach to this topic based on geometric invariant theory.

This is an outgrow from last year Cornell SPUR project with the collaboration of Pok-Wai Fong, Alex Frederick, Max Hallgreen, Hari-Rau Murthy, Kendric Schefers, Chris Strohmeier and Kaavya Valiveti.