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- W4300877552 abstract "Let $F$ be a non-Archimedean locally compact field. We show that the local Langlands correspondence over $F$ has a strong property generalizing the higher ramification theorem of local class field theory. If $pi$ is an irreducible cuspidal representation of a general linear group $GL_n(F)$ and $sigma$ the corresponding irreducible representation of the Weil group $W_F$ of $F$, the restriction of $sigma$ to a ramification subgroup of $W_F$ is determined by a truncation of the simple character $theta_pi$ contained in $pi$, and conversely. Numerical aspects of the relation are governed by a Herbrand-like function $Psi_Theta$ depending on the endo-class $Theta$ of $theta_pi$. We give a method for determining $Psi_Theta$. Consequently, the ramification-theoretic structure of $sigma$ can be predicted from the simple character $theta_pi$ alone." @default.
- W4300877552 created "2022-10-04" @default.
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- W4300877552 date "2015-10-06" @default.
- W4300877552 modified "2023-09-26" @default.
- W4300877552 title "Higher ramification and the local Langlands correspondence" @default.
- W4300877552 doi "https://doi.org/10.48550/arxiv.1510.01528" @default.
- W4300877552 hasPublicationYear "2015" @default.
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