July 1, 2024Open Access

Irreducible smooth representations in defining characteristic without central character

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Let p>3 and F be a non-archimedean local field with residue field a proper finite extension of Fₚ. Let E be an algebraically closed countable field extension of the residue field of F. In this short note, we explain how the methods from arXiv: 1809. 10247 and arXiv: 2210. 07281 can be used to construct irreducible smooth representations of GLₙ (F), n>1, over E without a central character.

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Daniel Le (Mon,) studied this question.

synapsesocial.com/papers/68e62291b6db6435875b4c67 https://doi.org/https://doi.org/10.48550/arxiv.2407.01766

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Irreducible smooth representations in defining characteristic without central character

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