\[ \DeclareMathOperator{\dim}{dim} \]

The dimension of \(\mathcal{H}_l\) is given by

\[ \dim \mathcal{H}_l = \dim \mathcal{H}_l^{\mathbb{C}} = \binom{d+l}{l} - \binom{d+l-2}{l-2} \]

[1, Corollary 1.5].

Links Link to heading

• spherical harmonic
• proof

References Link to heading

1. J. Gallier. Class Lecture, Topic: Notes on Spherical Harmonics and Linear Representations of Lie Groups.