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arXiv · 1905.01949

On Representations of Reductive $p$--adic Groups over $\mathbb Q$--algebras

Goran Muić
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Abstract

In this paper we study certain category of smooth modules for reductive $p$--adic groups analogous to the usual smooth complex representations but with the field of complex numbers replaced by a $\mathbb Q$--algebra. We prove some fundamental results in these settings, and as an example we give a classification of admissible unramified irreducible representations proving by reduction to the complex case that if the space of $K$--invariants is finite dimensional in an irreducible smooth unramified representation that the representation is admissible.

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Goran Muić. 2019-05-06. On Representations of Reductive $p$--adic Groups over $\mathbb Q$--algebras. https://arxiv.org/abs/1905.01949

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