Guy Henniart's Books

The Local Langlands Conjecture for GL(2)

By: Colin J. Bushnell,Guy Henniart

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The Local Langlands Conjecture for GL(2)

By: Colin J. Bushnell,Guy Henniart

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.

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Page Count

352

Publisher

Springer Science & Business Media

Published Date

ISBN 10

354031511X

ISBN 13

9783540315117

To an Effective Local Langlands Correspondence

By: Colin J. Bushnell,Guy Henniart

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To an Effective Local Langlands Correspondence

By: Colin J. Bushnell,Guy Henniart

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.

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Page Count

100

Publisher

American Mathematical Soc.

Published Date

ISBN 10

082189417X

ISBN 13

9780821894170

The Local Langlands Conjecture for GL(2)

By: Colin J. Bushnell,Guy Henniart

Write a review Read reviews Take a Quiz Solve Book Puzzle

The Local Langlands Conjecture for GL(2)

By: Colin J. Bushnell,Guy Henniart

Average ratings

N/A

Write a review

Solve jigsaw puzzle

Age

Page Count

352

Publisher

Springer Science & Business Media

Published Date

ISBN 10

354031511X

ISBN 13

9783540315117

To an Effective Local Langlands Correspondence

By: Colin J. Bushnell,Guy Henniart

Write a review Read reviews Take a Quiz Solve Book Puzzle

To an Effective Local Langlands Correspondence

By: Colin J. Bushnell,Guy Henniart

Average ratings

N/A

Write a review

Solve jigsaw puzzle

Age

Page Count

100

Publisher

American Mathematical Soc.

Published Date

ISBN 10

082189417X

ISBN 13

9780821894170

Book's by Guy Henniart

The Local Langlands Conjecture for GL(2)

The Local Langlands Conjecture for GL(2)

To an Effective Local Langlands Correspondence

To an Effective Local Langlands Correspondence

The Local Langlands Conjecture for GL(2)

The Local Langlands Conjecture for GL(2)

To an Effective Local Langlands Correspondence

To an Effective Local Langlands Correspondence

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