The Local Langlands Conjecture for GL(2) - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook The Local Langlands Conjecture for GL(2) write by Colin J. Bushnell. This book was released on 2006-08-29. The Local Langlands Conjecture for GL(2) available in PDF, EPUB and Kindle. The Local Langlands Conjecture for GL(2) contributes an unprecedented text to the so-called Langlands theory. It is an ambitious research program of already 40 years and gives a complete and self-contained proof of the Langlands conjecture in the case n=2. It is aimed at graduate students and at researchers in related fields. It presupposes no special knowledge beyond the beginnings of the representation theory of finite groups and the structure theory of local fields.
On the Local Langlands Conjecture for GL(2)
On the Local Langlands Conjecture for GL(2) - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook On the Local Langlands Conjecture for GL(2) write by Jerrold Bates Tunnell. This book was released on 1977. On the Local Langlands Conjecture for GL(2) available in PDF, EPUB and Kindle.
Representation Theory and Number Theory in Connection with the Local Langlands Conjecture
Representation Theory and Number Theory in Connection with the Local Langlands Conjecture - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Representation Theory and Number Theory in Connection with the Local Langlands Conjecture write by Jürgen Ritter. This book was released on 1989. Representation Theory and Number Theory in Connection with the Local Langlands Conjecture available in PDF, EPUB and Kindle. The Langlands Program summarizes those parts of mathematical research belonging to the representation theory of reductive groups and to class field theory. These two topics are connected by the vision that, roughly speaking, the irreducible representations of the general linear group may well serve as parameters for the description of all number fields. In the local case, the base field is a given $p$-adic field $K$ and the extension theory of $K$ is seen as determined by the irreducible representations of the absolute Galois group $G_K$ of $K$. Great progress has been made in establishing correspondence between the supercuspidal representations of $GL(n,K)$ and those irreducible representations of $G_K$ whose degrees divide $n$. Despite these advances, no book or paper has presented the different methods used or even collected known results. This volume contains the proceedings of the conference ``Representation Theory and Number Theory in Connection with the Local Langlands Conjecture,'' held in December 1985 at the University of Augsburg. The program of the conference was divided into two parts: (i) the representation theory of local division algebras and local Galois groups, and the Langlands conjecture in the tame case; and (ii) new results, such as the case $n=p$, the matching theorem, principal orders, tame Deligne representations, classification of representations of $GL(n)$, and the numerical Langlands conjecture. The collection of papers in this volume provides an excellent account of the current state of the local Langlands Program.
Automorphic Forms on GL (2)
Automorphic Forms on GL (2) - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Automorphic Forms on GL (2) write by H. Jacquet. This book was released on 2006-11-15. Automorphic Forms on GL (2) available in PDF, EPUB and Kindle.
To an Effective Local Langlands Correspondence
To an Effective Local Langlands Correspondence - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook To an Effective Local Langlands Correspondence write by Colin J. Bushnell. This book was released on 2014-08-12. To an Effective Local Langlands Correspondence available in PDF, EPUB and Kindle. 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 _{n\ge 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 "naïve 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.
