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# đź“™ The Local Langlands Conjecture for GL(2) by Colin J. Bushnell, Guy Henniart (auth.) â€” free epub

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If F is a non-Archimedean local field, local class field theory can be viewed as giving a canonical bijection between the characters of the multiplicative group GL(1,F) of F and the characters of the Weil group of F. If n is a positive integer, the n-dimensional analogue of a character of the multiplicative group of F is an irreducible smooth representation of the general linear group GL(n,F). The local Langlands Conjecture for GL(n) postulates the existence of a canonical bijection between such objects and n-dimensional representations of the Weil group, generalizing class field theory.

This conjecture has now been proved for all F and n, but the arguments are long and rely on many deep ideas and techniques. This book 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. It uses only local methods, with no appeal to harmonic analysis on adele groups.

- Series:
**Grundlehren der mathematischen Wissenschaften 335** - Author:
**Colin J. Bushnell, Guy Henniart (auth.)** - Year:
**2006** - Publisher:
**Springer-Verlag Berlin Heidelberg** - Language:
**English** - ISBN:
**9783540314868,3-540-31486-5**

- File size:
**2 981 679** - Format:
**pdf**

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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 representa...

The authors construct new families of smooth admissible $\overline{\mathbb{F}}_p$-representations of $\mathrm{GL}_2(F)$, where $F$ is a finite extension of $\mathbb{Q}_p$. When $F$ is unramified, these representations have the $\mathrm{GL}_2({\mathcal O}_...

Restenosis remains the Achilles heel of Percutaneous Coronary Interventions. Numerous pharmacological agents have been tested in order to reduce acute thrombosis and the hyperproliferative cellular response, and drug eluting stents-using the stent as a pl...

Vitushkin's conjecture, a special case of PainlevĂ©'s problem, states that a compact subset of the complex plane with finite linear Hausdorff measure is removable for bounded analytic functions if and only if it intersects every rectifiable curve in a set ...

In this publication the necessity of activation and building local resources needed for recovery and development is highlighted at the level of individuals, social systems and structures, social networks, civil society and at the level of the community in...

Vitushkin's conjecture, a special case of PainlevĂ©'s problem, states that a compact subset of the complex plane with finite linear Hausdorff measure is removable for bounded analytic functions if and only if it intersects every rectifiable curve in a set ...

For the past several decades the theory of automorphic forms has become a major focal point of development in number theory and algebraic geometry, with applications in many diverse areas, including combinatorics and mathematical physics. The twelve chapt...

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 represe...

These lecture notes contain a guided tour to the Novikov Conjecture and related conjectures due to Baum-Connes, Borel and Farrell-Jones. They begin with basics about higher signatures, Whitehead torsion and the s-Cobordism Theorem. Then an introduction to...

In the aftermath of the English Civil War, as people were groping for new forms of political order, Robert Boyle built an air-pump to do exper???iments. Does the story of Roundheads and Restoration have something to do with the origins of experimental sci...

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The taloids, the alien robots who inhabited Titan, Saturn's largest moon, had succeeded in preserving their own freedom against both greedy humans from Earth and their own home-grown despots, but now they have discovered strange blocks of code, hidden for...

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Since 1948, this serial has sought to fill the gap between the papers and the textbooks that teach the diverse areas of catalysis research. This volume includes articles on the applications of adsorption microcalorimetry and organic syntheses using alumin...

This series, established in 1965, is concerned with recent developments in the general area of atomic, molecular and optical physics. The field is in a state of rapid growth, as new experimental and theoretical techniques are put to bear on many old and n...

The EU accession process will shape Turkey's future and, in particular, its potential to become a pluralist, democratic state with respect for international human rights. In this timely survey Kerim Yildiz and Mark Muller explain and analyse the process o...

Whether providing automated passenger transport systems, exploring the hostile depths of the ocean or assisting soldiers in battle, autonomous vehicle systems are becoming an important fact of modern life. Distributed sensing and communication networks al...