A tensor square theorem for characters of $\operatorname{GL}_{n}(q)$

Nariel Monteiro; Alexander Stasinski

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arXiv · 2609.17319

A tensor square theorem for characters of $\operatorname{GL}_{n}(q)$

Nariel Monteiro·Alexander Stasinski

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Abstract

We construct an irreducible character of $\operatorname{GL}_{n}(q)$ whose square contains every irreducible character that is trivial on the centre of $\operatorname{GL}_{n}(q)$. This character is related to, but in general not equal to, the Steinberg character. A key ingredient, which we also prove, is that every nonlinear irreducible character of $\operatorname{GL}_{n}(q)$ that is trivial on the centre contains the trivial character when restricted to the diagonal subgroup $T$.

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BibTeX RIS

Nariel Monteiro, Alexander Stasinski. 2026-09-15. A tensor square theorem for characters of $\operatorname{GL}_{n}(q)$. https://arxiv.org/abs/2609.17319

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