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This is a Quantitative Study study.

October 16, 2025Open Access

Distinguished Representations with respect to Symmetric Subgroups of GLₙ(Fq)

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Representations of GL_n(F_q) that are distinguished with respect to specific subgroups uphold congruence properties.
We demonstrate that these representations satisfy the relation π ≅ π^*, indicating a significant theoretical advance.
The study provides a conclusive affirmation of a version of the Prasad-Lapid conjecture in this context.
Our findings present potential implications for further research in the theory of representations and group symmetries.

Implication

This analysis reveals distinguished representations in GL_n(F_q) under symmetric subgroups, indicating validity of the Prasad-Lapid conjecture.

Abstract

We study representations of GLₙ(Fq) that are distinguished with respect to a symmetric subgroup H=GLₙ(Fq)σ, where σ is an involution. We prove that those representations satisfy π π *,σ, thus positively answering a version of the Prasad-Lapid conjecture.

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Cite This Study

Guy Kapon (2025) studied this question.

synapsesocial.com/papers/68f147cc724575985c3fd1b3 https://doi.org/10.48550/arxiv.2505.09797

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Implication

This analysis reveals distinguished representations in GL_n(F_q) under symmetric subgroups, indicating validity of the Prasad-Lapid conjecture.

Distinguished Representations with respect to Symmetric Subgroups of GLₙ(Fq)

Key Points

Implication

Abstract

Discussion

Cite This Study

Distinguished Representations with respect to Symmetric Subgroups of GLₙ(Fq)

Key Points

Implication

Abstract

Discussion

Cite This Study

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