Is there an explicit way to identify the space of spherical harmonics and the space of homogeneous polynomials over $\mathbb{C}^2$?
I know that the space of spherical harmonics can be seen the irreducible representation of $SO(3)$. Is there a way to identify the space geometrically?
I was taking of using the map $\mathbb{C}^2 \rightarrow \mathbb{P}^1$. But I'm not super familiar with geometry.
Any help will be appreciated!