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On some crystalline representations of \(\mathrm{GL}_2(\mathbb Q_p)\). (English) Zbl 1173.22015

It is proved that if \(G:= \mathrm{GL}_2(\mathbb Q_p)\) with \(p > 2\), then the universal unitary completion of some locally algebraic representation of \(G\) is topologically irreducible, admissible, and corresponds to a two-dimensional irreducible crystalline representation with non-simple Frobenius via the \(p\)-adic Langlands correspondence for \(G\).

MSC:

22E50 Representations of Lie and linear algebraic groups over local fields
11S37 Langlands-Weil conjectures, nonabelian class field theory
11S20 Galois theory