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arXiv · 2412.10797

Orthogonal Determinants of $\mathrm{GL}_n(q)$

Linda Hoyer
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Abstract

Let $n$ be a positive integer and $q$ be a power of an odd prime. We provide explicit formulas for calculating the orthogonal determinants $\det(\chi)$, where $\chi \in \mathrm{Irr}(\mathrm{GL}_n(q))$ is an orthogonal character of even degree. Moreover, we show that $\det(\chi)$ is "odd". This confirms a special case of a conjecture by Richard Parker.

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Linda Hoyer. 2024-12-14. Orthogonal Determinants of $\mathrm{GL}_n(q)$. https://arxiv.org/abs/2412.10797

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