Representations with the same degree
Representation Theory
2026-02-24 v2
Abstract
In this short note we show that every connected reductive simply-connected algebraic group of rank 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.
Cite
@article{arxiv.2601.18786,
title = {Representations with the same degree},
author = {Frank Lübeck},
journal= {arXiv preprint arXiv:2601.18786},
year = {2026}
}
Comments
Corrected notation for G_2 to Bourbaki convention. Added a few remarks in the end