Admissible Invariant Distributions on Reductive $p$-adic Groups (eBook)

Harish-Chandra (Autor)

eBook Download: PDF

2015
97 Seiten
American Mathematical Society (Verlag)
978-1-4704-2165-6 (ISBN)

Infos

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 "e;Queen's Notes"e;. 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.

Produkt-Details

• Erscheint lt. Verlag: 2.1.2015
• Themenwelt: Mathematik / Informatik ► Mathematik ► Algebra
• Themenwelt: Mathematik / Informatik ► Mathematik ► Analysis
• ISBN-10: 1-4704-2165-8 / 1470421658
• ISBN-13: 978-1-4704-2165-6 / 9781470421656