ADMISSIBLE INVARIANT DISTRIBUTIONS ON REDUCTIVE P-ADIC GROUPS by Chandra Harish ( 9780821820254 )

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Title:

ADMISSIBLE INVARIANT DISTRIBUTIONS ON REDUCTIVE P-ADIC GROUPS

By:

Format:

Paperback

List price:	£61.00
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ISBN 10:

0821820257

ISBN 13:

9780821820254

Publisher:

AMERICAN MATHEMATICAL SOCIETY

Pub. date:

15 July, 1999

Series:

University Lecture Series No. 16

Pages:

Description:

Harish-Chandra's remarkable theorem on the local summability of characters for $p$-adic groups was a major result in representation theory that spawned many other significant results. This book presents a complete account of Harish-Chandra's original lectures on this subject, including his extension and proof of Howe's Theorem.

Synopsis:

Harish-Chandra presented these lectures on admissible invariant distributions for $p$-adic groups at the Institute for Advanced Study in the early 1970s. He published a short sketch of this material as his famous ""Queen's Notes"". This book, which was prepared and edited by DeBacker and Sally, presents a faithful rendering of Harish-Chandra's original lecture notes. 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 $\mathfrak g$, the Lie algebra of $G$. In particular, Harish-Chandra shows that if the support of a $G$-invariant distribution on $\mathfrak g$ is compactly generated, then its Fourier transform has an asymptotic expansion about any semisimple point of $\mathfrak g$.Harish-Chandra's remarkable theorem on the local summability of characters for $p$-adic groups was a major result in representation theory that spawned many other significant results.This book presents, for the first time in print, a complete account of Harish-Chandra's original lectures on this subject, including his extension and proof of Howe's Theorem. In addition to the original Harish-Chandra notes, DeBacker and Sally provide a nice summary of developments in this area of mathematics since the lectures were originally delivered. In particular, they discuss quantitative results related to the local character expansion.

Publication:

Imprint:

American Mathematical Society

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Returnable

Some other items by this author:

COLLECTED PAPERS (PB)

COLLECTED PAPERS I (PB)

COLLECTED PAPERS II (PB)

COLLECTED PAPERS III (PB)

COLLECTED PAPERS IV (PB)

LECTURES IN MODERN ANALYSIS AND APPLICATIONS II (PB)