To an Effective Local Langlands Correspondence
Book Title: To an Effective Local Langlands Correspondence Category: Science & Geography Language: English Realese Date: 1 September 2014 Number of Pages: 88 pages Autor: Colin J. Bushnell ISBN: 9780821894170 |
Description of the book "To an Effective Local Langlands Correspondence"
Let $F$ be a non-Archimedean local field. Let $mathcal{W}_{F}$ be the Weil group of $F$ and $mathcal{P}_{F}$ the wild inertia subgroup of $mathcal{W}_{F}$. Let $widehat {mathcal{W}}_{F}$ be the set of equivalence classes of irreducible smooth representations of $mathcal{W}_{F}$. Let $mathcal{A}^{0}_{n}(F)$ denote the set of equivalence classes of irreducible cuspidal representations of $mathrm{GL}_{n}(F)$ and set $widehat {mathrm{GL}}_{F} = bigcup _{nge 1} mathcal{A}^{0}_{n}(F)$. If $sigma in widehat {mathcal{W}}_{F}$, let $^{L}{sigma }in widehat {mathrm{GL}}_{F}$ be the cuspidal representation matched with $sigma$ by the Langlands Correspondence. If $sigma$ is totally wildly ramified, in that its restriction to $mathcal{P}_{F}$ is irreducible, the authors treat $^{L}{sigma}$ as known. From that starting point, the authors construct an explicit bijection $mathbb{N}:widehat {mathcal{W}}_{F} to widehat {mathrm{GL}}_{F}$, sending $sigma$ to $^{N}{sigma}$. The authors compare this "naive correspondence" with the Langlands correspondence and so achieve an effective description of the latter, modulo the totally wildly ramified case. A key tool is a novel operation of "internal twisting" of a suitable representation $pi$ (of $mathcal{W}_{F}$ or $mathrm{GL}_{n}(F)$) by tame characters of a tamely ramified field extension of $F$, canonically associated to $pi$. The authors show this operation is preserved by the Langlands correspondence.You can buy and download To an Effective Local Langlands Correspondence in PDF, EPUB, TXT, DOC and other versions in most online book stores - e.g. on www.amazon.com. |