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arXiv · 2601.18786

Representations with the same degree

Frank Lübeck
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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.

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Frank Lübeck. 2026-01-26. Representations with the same degree. https://arxiv.org/abs/2601.18786

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