Pointwise character bounds for $\mathrm{SU}(3)$

TL;DR

This paper establishes pointwise bounds for irreducible characters of SU(3) and derives new L^p bounds using character descent and cancellation techniques.

Contribution

It introduces a novel pointwise bound for SU(3) characters and applies it to obtain improved L^p bounds, advancing understanding of representation bounds.

Findings

Established a basic pointwise bound for SU(3) characters.

Derived new L^p bounds for these characters.

Used descent to singular sets and cancellation in the analysis.

Abstract

We present a basic pointwise bound for the irreducible characters of $\mathrm{SU}(3)$ and, as an application, derive new $L^p$ bounds for these characters. Our approach is based on the descent of characters to singular sets and the cancellation in this formula.