An asymptotic formula for the number of $n$-dimensional representations of $\mathrm{SU}(3)$

TL;DR

This paper derives an asymptotic formula for counting n-dimensional representations of the group SU(3), using Wright's Circle Method and the Saddle Point Method to analyze the growth rate.

Contribution

It introduces a novel asymptotic formula for the enumeration of n-dimensional representations of SU(3), employing advanced analytic techniques.

Findings

Established an explicit asymptotic expression for the count of representations.

Applied Wright's Circle Method and Saddle Point Method to a group representation problem.

Enhanced understanding of the growth behavior of SU(3) representations.

Abstract

We prove an asymptotic formula for the number of $n$-dimensional representations of the group $\mathrm{SU}(3)$. Main tools for the proof are Wright's Circle Method and the Saddle Point Method.