# Download E-books To an Effective Local Langlands Correspondence (Memoirs of the American Mathematical Society) PDF

Enable $F$ be a non-Archimedean neighborhood box. allow $\mathcal{W}_{F}$ be the Weil team of $F$ and $\mathcal{P}_{F}$ the wild inertia subgroup of $\mathcal{W}_{F}$. permit $\widehat {\mathcal{W}}_{F}$ be the set of equivalence periods of irreducible soft representations of $\mathcal{W}_{F}$. enable $\mathcal{A}^{0}_{n}(F)$ denote the set of equivalence sessions of irreducible cuspidal representations of $\mathrm{GL}_{n}(F)$ and set $\widehat {\mathrm{GL}}_{F} = \bigcup _{n\ge 1} \mathcal{A}^{0}_{n}(F)$. If $\sigma \in \widehat {\mathcal{W}}_{F}$, enable $^{L}{\sigma }\in \widehat {\mathrm{GL}}_{F}$ be the cuspidal illustration matched with $\sigma$ through the Langlands Correspondence. If $\sigma$ is completely wildly ramified, in that its limit to $\mathcal{P}_{F}$ is irreducible, the authors deal with $^{L}{\sigma}$ as identified. From that start line, the authors build an particular bijection $\mathbb{N}:\widehat {\mathcal{W}}_{F} \to \widehat {\mathrm{GL}}_{F}$, sending $\sigma$ to $^{N}{\sigma}$. The authors examine this "naive correspondence" with the Langlands correspondence and so in achieving a good description of the latter, modulo the utterly wildly ramified case. A key instrument is a unique operation of "internal twisting" of an appropriate illustration $\pi$ (of $\mathcal{W}_{F}$ or $\mathrm{GL}_{n}(F)$) by means of tame characters of a tamely ramified box extension of $F$, canonically linked to $\pi$. The authors convey this operation is preserved via the Langlands correspondence.

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