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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:
 2.2e+51 Representations of Lie and linear algebraic groups over local fields
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