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- W2998681609 abstract "We consider the restriction to $SL_2({mathbb Q}_p)$ of an irreducible $p$-adic unitary Banach space representation $Pi$ of $GL_2({mathbb Q}_p)$. If $Pi$ is associated, via the $p$-adic local Langlands correspondence, to an absolutely irreducible 2-dimensional Galois representation $psi$, then the restriction of $Pi$ decomposes as a direct sum of $r le 2$ irreducible representations. The main result of this paper is that $r$ is equal to the cardinality $s$ of the centralizer in $PGL_2$ of the projective Galois representation $overline{psi}$ associated to $psi$, and the restriction is multiplicity-free, except if $psi$ is triply-imprimitive, in which case the restriction of $Pi$ is a direct sum of two equivalent representations. From this result we derive a classification of absolutely irreducible $p$-adic unitary Banach space representations of $SL_2({mathbb Q}_p)$." @default.
- W2998681609 created "2020-01-10" @default.
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- W2998681609 date "2019-12-23" @default.
- W2998681609 modified "2023-09-27" @default.
- W2998681609 title "$p$-adic Banach space representations of $SL_2({mathbb Q}_p)$" @default.
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