Admissible Invariant Distributions on Reductive P-Adic Groups - Couverture souple

American Mathematical Society

Couverture souple

ISBN 10 : 0821820257 ISBN 13 : 9780821820254

Editeur : American Mathematical Society, 1999

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.

Détails de l'édition

• Éditeur: American Mathematical Society
• Date d'édition: 1999
• Langue: anglais
• ISBN 10: 0821820257
• ISBN 13: 9780821820254
• Reliure: Broché
• Nombre de pages: 97
• Coordonnées du fabricant: non disponible
• Personne responsable: non disponible