{"product_id":"unipotent-ideals-and-harish-chandra-bimodules-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\u003cbr\u003e\u003cbr\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).\u003cbr\u003e\u003cbr\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.\u003c\/p\u003e","brand":"Ivan Loseu","offers":[{"title":"Default Title","offer_id":43489689075830,"sku":"9780691294490","price":75.0,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0671\/1374\/6550\/files\/CoreSourceHub_6e1f92f9-3789-4a0f-9c6b-73c3a73886b7.jpg?v=1780869686","url":"https:\/\/ingramacademic.com\/products\/unipotent-ideals-and-harish-chandra-bimodules-9780691294490","provider":"Ingram Academic \u0026 Professional","version":"1.0","type":"link"}