{"product_id":"admissible-invariant-distributions-on-reductive-p-adic-groups","title":"Admissible Invariant Distributions on Reductive P-adic Groups","description":"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.","brand":"American Mathematical Society","offers":[{"title":"Default Title","offer_id":57186476261720,"sku":"9780821820254","price":71.99,"currency_code":"EUR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0278\/1295\/4195\/files\/9780821820254_b3b08132-7b40-4b42-87ed-79005caab90a.jpg?v=1780110947","url":"https:\/\/agendabookshop.com\/products\/admissible-invariant-distributions-on-reductive-p-adic-groups","provider":"Agenda Bookshop","version":"1.0","type":"link"}