{"product_id":"unipotent-ideals-and-harish-chandra-bimodules-ivan-loseu-9780691294490","title":"Unipotent Ideals and Harish-Chandra Bimodules","description":"\u003cp\u003e\u003cb\u003eA groundbreaking book that applies new geometric tools to one of the oldest problems in representation theory, expanding the field and paving the way for further progress\u003c\/b\u003e \u003c\/p\u003e\u003cp\u003e\u003c\/p\u003eIn the 1920s, Hermann Weyl gave a complete classification of the irreducible unitary representations of a compact Lie group G. Around the same time, Fritz Peter and Weyl showed that these irreducible unitary representations are fundamental objects for harmonic analysis on G. If G is instead a \u003ci\u003enoncompact\u003c\/i\u003e Lie group, such as GL_n(R), the classification of the irreducible unitary G-representations is a much more difficult problem, one that remains open in general. An idea, with its origins in the work of Kostant, Kirillov, and Vogan, is that the set of irreducible unitary G-representations should contain a finite set of \"building blocks,\" called unipotent representations, related to the set of nilpotent co-adjoint G-orbits. This book proposes a definition and theory of unipotent representations in the case of when G is a complex reductive Lie group, such as GL_n(C). \u003cp\u003e\u003c\/p\u003eThis definition is based on the theory of quantizations of symplectic singularities, especially the geometry of nilpotent co-adjoint orbits and their equivariant covers. The main theorems include a geometric classification of unipotent representations, a calculation of their infinitesimal characters, and a proof of their unitarity in the case of classical groups. Although further obstacles remain, this work paves the way for a general theory of unipotent representations of reductive Lie groups, which should in turn form the basis of the classification of irreducible unitary representations.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eAuthor:\u003c\/b\u003e Ivan Loseu,Dmytro Matvieievskyi,Lucas Mason-Brown\u003cbr\u003e\u003cb\u003eISBN-10:\u003c\/b\u003e 0691294496\u003cbr\u003e\u003cb\u003eISBN-13:\u003c\/b\u003e 9780691294490\u003cbr\u003e\u003cb\u003ePublisher:\u003c\/b\u003e Princeton University Press\u003cbr\u003e\u003cb\u003eLanguage:\u003c\/b\u003e English\u003cbr\u003e\u003cb\u003ePublished:\u003c\/b\u003e 01\/12\/2027\u003cbr\u003e\u003cb\u003ePages:\u003c\/b\u003e 280\u003cbr\u003e\u003cb\u003eFormat:\u003c\/b\u003e Paperback","brand":"Ivan Loseu","offers":[{"title":"Paperback","offer_id":48997645123839,"sku":"9780691294490","price":75.0,"currency_code":"USD","in_stock":false}],"url":"https:\/\/www.whiterainbookhouse.com\/products\/unipotent-ideals-and-harish-chandra-bimodules-ivan-loseu-9780691294490","provider":"WR Book House","version":"1.0","type":"link"}