Admissible invariant distributions on reductive p-adic groups

de Harish-Chandra.

"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."--Jacket. "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.