Representations with the same degree

Abstract

In this short note we show that every connected reductive simply-connected algebraic group of rank $>1$ over the complex numbers has infinitely many pairs of irreducible representations which are not related by an automorphism of the algebraic group and which have the same degree. This answers a question I was asked by J.~P.~Serre.

Corrected notation for G_2 to Bourbaki convention. Added a few remarks in the end