Colin J. Bushnell'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

The Admissible Dual of GL(N) via Compact Open Subgroups. (AM-129), Volume 129

By: C. Bushnell,P. C. Kutzko

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The Admissible Dual of GL(N) via Compact Open Subgroups. (AM-129), Volume 129

By: C. Bushnell,P. C. Kutzko

This work gives a full description of a method for analyzing the admissible complex representations of the general linear group G = Gl(N,F) of a non-Archimedean local field F in terms of the structure of these representations when they are restricted to certain compact open subgroups of G. The authors define a family of representations of these compact open subgroups, which they call simple types. The first example of a simple type, the "trivial type," is the trivial character of an Iwahori subgroup of G. The irreducible representations of G containing the trivial simple type are classified by the simple modules over a classical affine Hecke algebra. Via an isomorphism of Hecke algebras, this classification is transferred to the irreducible representations of G containing a given simple type. This leads to a complete classification of the irreduc-ible smooth representations of G, including an explicit description of the supercuspidal representations as induced representations. A special feature of this work is its virtually complete reliance on algebraic methods of a ring-theoretic kind. A full and accessible account of these methods is given here.

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Page Count

332

Publisher

Princeton University Press

Published Date

ISBN 10

1400882494

ISBN 13

9781400882496

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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100

Publisher

American Mathematical Soc.

Published Date

ISBN 10

082189417X

ISBN 13

9780821894170

The California Electricity Crisis

What, Why, and What’s Next

By: Charles J. Cicchetti,Jeffrey A. Dubin,Colin M. Long

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The California Electricity Crisis

What, Why, and What’s Next

By: Charles J. Cicchetti,Jeffrey A. Dubin,Colin M. Long

This book attempts to explain what went wrong in California’s restructured energy markets and what must be done to restore California’s economy and build new electricity systems. The intention here is to reconcile the principles of competition and regulation. California had a severe electricity crisis for about thirteen months beginning in May of 2000. The economic consequences and political fallout that arose from this crisis persist. California’s economy continues to suffer and the state’s treasury is deeply in debt. The state’s three investor-owned utilities were nearly financially decimated. San Diego Gas & Electric has recovered to a greater degree than the other two only because its retail prices are about three times the national average and, for a time, well above the other two IOUs in California. Southern California Edison has recently been restored to investment grade and was granted a rate increase. Pacific Gas & Electric is emerging from bankruptcy. This book discusses all of this in greater detail. The problems and consequences arising from California’s ill-fated foray into electricity market restructuring could damage the state for years to come. Challenges of this nature are not new to the Golden State. In the past, as we explain here, pragmatic, not entrenched, approaches have worked best in California. If California is to relatively quickly restore its previous enviable economic vitality and recover from the damage done to tarnish its luster, pragmatic approaches must again be used.

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Page Count

214

Publisher

Springer Science & Business Media

Published Date

ISBN 10

1402080328

ISBN 13

9781402080326

Book's by Colin J. Bushnell

The Local Langlands Conjecture for GL(2)

The Local Langlands Conjecture for GL(2)

The Admissible Dual of GL(N) via Compact Open Subgroups. (AM-129), Volume 129

The Admissible Dual of GL(N) via Compact Open Subgroups. (AM-129), Volume 129

To an Effective Local Langlands Correspondence

To an Effective Local Langlands Correspondence

The California Electricity Crisis

The California Electricity Crisis

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