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| Author | : David Goldberg |
| Publisher | : |
| Total Pages | : 52 |
| Release | : 1995 |
| Genre | : |
| ISBN | : |
| Author | : Clifton Cunningham |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 217 |
| Release | : 2009-01-01 |
| Genre | : Mathematics |
| ISBN | : 0821885944 |
| Author | : |
| Publisher | : |
| Total Pages | : 199 |
| Release | : 2009 |
| Genre | : Electronic books |
| ISBN | : 9781470417895 |
Ottawa Lectures offers researchers and graduate students a rare introduction to some of the major modern themes in the representation theory of p-adic groups: the classification and construction of their (complex) admissible representations, the calculation of their characters, and the realization of the celebrated local Langlands correspondence. Recent years have seen significant and rapid progress made toward each of these goals; the purpose of this book is to help bridge the gap from the classical literature to the forefront of research. The first part of this volume is devoted to the tools.
| Author | : Anne-Marie Aubert |
| Publisher | : Springer |
| Total Pages | : 289 |
| Release | : 2019-04-16 |
| Genre | : Mathematics |
| ISBN | : 9811366284 |
This book consists of survey articles and original research papers in the representation theory of reductive p-adic groups. In particular, it includes a survey by Anne-Marie Aubert on the enormously influential local Langlands conjectures. The survey gives a precise and accessible formulation of many aspects of the conjectures, highlighting recent refinements, due to the author and her collaborators, and their current status. It also features an extensive account by Colin Bushnell of his work with Henniart on the fine structure of the local Langlands correspondence for general linear groups, beginning with a clear overview of Bushnell–Kutzko’s construction of cuspidal types for such groups. The remaining papers touch on a range of topics in this active area of modern mathematics: group actions on root data, explicit character formulas, classification of discrete series representations, unicity of types, local converse theorems, completions of Hecke algebras, p-adic symmetric spaces. All meet a high level of exposition. The book should be a valuable resource to graduate students and experienced researchers alike.
| Author | : Eng-chye Tan |
| Publisher | : World Scientific |
| Total Pages | : 426 |
| Release | : 2004 |
| Genre | : Mathematics |
| ISBN | : 9812562508 |
This invaluable volume collects the expanded lecture notes of thosetutorials. The topics covered include uncertainty principles forlocally compact abelian groups, fundamentals of representations of"p"-adic groups, the Harish?Chandra?Howe local characterexpansion, classification of the square-integrable representationsmodulo cuspidal data, Dirac cohomology and Vogan's conjecture, multiplicity-free actions and Schur?Weyl?Howe duality.
| Author | : Harish-Chandra |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 113 |
| Release | : 1999 |
| Genre | : Mathematics |
| ISBN | : 0821820257 |
"The main purpose of Harish-Chandra's lectures was to show that the character of an irreducible admissible representation of a connected reductive p-adic group G is represented by a locally summable function on G.A key ingredient in this proof is the study of the Fourier transforms of distributions on g, the Lie algebra of G. In particular, Harish-Chandra shows that if the support of a G-invariant distribution on g is compactly generated, then its Fourier transform has an asymptotic expansion about any semisimple point of g."--Jacket.
| Author | : |
| Publisher | : |
| Total Pages | : 584 |
| Release | : 2008 |
| Genre | : Mathematics |
| ISBN | : |
| Author | : Ecole normale supérieure (France) |
| Publisher | : |
| Total Pages | : 1088 |
| Release | : 2006 |
| Genre | : Electronic journals |
| ISBN | : |
| Author | : Caterina Consani |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 374 |
| Release | : 2007-12-18 |
| Genre | : Mathematics |
| ISBN | : 3834803529 |
In recent years, number theory and arithmetic geometry have been enriched by new techniques from noncommutative geometry, operator algebras, dynamical systems, and K-Theory. This volume collects and presents up-to-date research topics in arithmetic and noncommutative geometry and ideas from physics that point to possible new connections between the fields of number theory, algebraic geometry and noncommutative geometry. The articles collected in this volume present new noncommutative geometry perspectives on classical topics of number theory and arithmetic such as modular forms, class field theory, the theory of reductive p-adic groups, Shimura varieties, the local L-factors of arithmetic varieties. They also show how arithmetic appears naturally in noncommutative geometry and in physics, in the residues of Feynman graphs, in the properties of noncommutative tori, and in the quantum Hall effect.
| Author | : Robert S. Doran |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 568 |
| Release | : 2000 |
| Genre | : Mathematics |
| ISBN | : 0821811975 |
Harish-Chandra was a mathematician of great power, vision, and remarkable ingenuity. His profound contributions to the representation theory of Lie groups, harmonic analysis, and related areas left researchers a rich legacy that continues today. This book presents the proceedings of an AMS Special Session entitled, "Representation Theory and Noncommutative Harmonic Analysis: A Special Session Honoring the Memory of Harish-Chandra", which marked 75 years since his birth and 15 years since his untimely death at age 60. Contributions to the volume were written by an outstanding group of internationally known mathematicians. Included are expository and historical surveys and original research papers. The book also includes talks given at the IAS Memorial Service in 1983 by colleagues who knew Harish-Chandra well. Also reprinted are two articles entitled, "Some Recollections of Harish-Chandra", by A. Borel, and "Harish-Chandra's c-Function: A Mathematical Jewel", by S. Helgason. In addition, an expository paper, "An Elementary Introduction to Harish-Chandra's Work", gives an overview of some of his most basic mathematical ideas with references for further study. This volume offers a comprehensive retrospective of Harish-Chandra's professional life and work. Personal recollections give the book particular significance. Readers should have an advanced-level background in the representation theory of Lie groups and harmonic analysis.
