On the number of irreducible representations of $\mathfrak{su}(3)$
Volume 215 / 2024
Acta Arithmetica 215 (2024), 65-71
MSC: Primary 11N45; Secondary 11N56, 17B05
DOI: 10.4064/aa230813-9-4
Published online: 27 May 2024
Abstract
We use a variant of the hyperbola method to prove an asymptotic expansion for the summatory function of the number of irreducible $\mathfrak{su}(3)$-representations of dimension $n$. This is a natural companion result to work of Romik, who proved an asymptotic formula for the number of unrestricted $\mathfrak{su}(3)$-representations of dimension $n$.
