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Admissible Invariant Distributions on Reductive P-Adic Groups
  • Bandtyp: Pocket
  • Språk: Engelska
  • Utgiven: 199907
  • Antal sidor: 97
  • Vikt i gram: 204
  • ISBN10:0821820257
  • ISBN13:9780821820254

Admissible Invariant Distributions on Reductive P-Adic Groups


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.

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