Conjectures and Results on Modular Representations of 𝐺𝐿👺 (𝐾) for a 𝑝-Adic Field 𝐾

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Conjectures reveal properties of modular representations in a p-adic field, suggesting connections with automorphic forms.

Modular representations exhibit complex relationships in a p-adic field, enhancing understanding of finite length.
Analysis gives insights into automorphic forms linked to compact unitary groups under modular representations.
Research confirms specific cases of conjectures regarding extensions and subquotients of representations when n=2.
These findings may enable developments in algebraic representation theory and applications in number theory.

Breuil et al. (2025) studied this question.

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Conjectures reveal properties of modular representations in a p-adic field, suggesting connections with automorphic forms.

Modular representations exhibit complex relationships in a p-adic field, enhancing understanding of finite length.
Analysis gives insights into automorphic forms linked to compact unitary groups under modular representations.
Research confirms specific cases of conjectures regarding extensions and subquotients of representations when n=2.
These findings may enable developments in algebraic representation theory and applications in number theory.

Breuil et al. (2025) studied this question.

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