On the number of irreducible representations of $\mathfrak{su}(3)$

TL;DR

This paper derives an asymptotic expansion for the total count of irreducible $rak{su}(3)$-representations of dimension n, complementing prior work on unrestricted representations, using a hyperbola method variant.

Contribution

It introduces a novel application of the hyperbola method to asymptotically analyze the summatory function of irreducible $rak{su}(3)$-representations.

Findings

Established an asymptotic expansion for the summatory function

Extended understanding of the distribution of irreducible $rak{su}(3)$-representations

Provided a natural complement to Romik's results

Abstract

In this note, 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 $n$.