Orthogonal Determinants of GL_n(q)

2024/12/14 by Linda Hoyer, Hoyer, Linda
Chemistry · Mathematics · #Advanced Algebra and Geometry #Advanced NMR Techniques and Applications #FOS: Mathematics #Finite Group Theory Research #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2412.10797

openalex publication_date 2024/12/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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(χ), where χ∈ Irr(GL_n(q)) is an orthogonal character of even degree. Moreover, we show that det(χ) is "odd". This confirms a special case of a conjecture by Richard Parker.

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