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On the restriction of representations of \(\text{GL}_2(F)\) to a Borel subgroup. (English) Zbl 1136.22010
This work aims to study the restriction of smooth irreducible representations of \(G=\text{GL}_2(F)\) on an \(\overline{\mathbf{F}}_p\)-vector space to \(P\), a Borel subgroup of \(G\), where \(F\) is a non-Archimedean local field and \(p\) is the residual characteristic of \(F\). It is particularly proved that to some degree, \(P\) controls the representations of \(G\).

MSC:
22E50 Representations of Lie and linear algebraic groups over local fields
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