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Geometry of GL n (ℂ) at Infinity: Hinges, Complete Collineations,Projective Compactifications, and Universal Boundary

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The Orbit Method in Geometry and Physics

Part of the book series: Progress in Mathematics ((PM,volume 213))

Abstract

Compactifications of semisimple groups and of homogeneous spaces arise in natural ways in different branches of mathematics (enumerative algebraic geometry, noncommutative harmonic analysis, automorphic forms, etc.). The most important construction of this kind is the family of objects called the Satake boundary or the De Concini-Procesi boundary or thewonderful compactification;see [26], [7], [4], [12], and [22]. For the first time, such compactifications of the group PGLn(ℂ) (the complete collineations) and of the symmetric space PGLn(ℂ)/POn(ℂ) (the complete quadrics) were discovered by Semple [27], [28], [29].

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Authors and Affiliations

  1. Bolshaya Cheremushkinskaya, Institute of Theoretical and Experimental Physics, 25 Moscow, 117259, Russia

    Yurii A. Neretin

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  1. Yurii A. Neretin
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Editors and Affiliations

  1. Centre de Physique Théorique CNRS, Campus de Luminy, Marseille Cedex 9, F-13288, France

    Christian Duval

  2. Institut Girard Desargues, Université Claude Bernard Lyon 1, Villeurbanne Cedex, F-69622, France

    Valentin Ovsienko

  3. Département des Sciences Mathématiques, Université Montpellier II, Montpelier Cedex 5, F-34095, France

    Laurent Guieu

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Neretin, Y.A. (2003). Geometry of GL n (ℂ) at Infinity: Hinges, Complete Collineations,Projective Compactifications, and Universal Boundary. In: Duval, C., Ovsienko, V., Guieu, L. (eds) The Orbit Method in Geometry and Physics. Progress in Mathematics, vol 213. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0029-1_13

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  • DOI: https://doi.org/10.1007/978-1-4612-0029-1_13

  • Publisher Name: Birkhäuser, Boston, MA

  • Print ISBN: 978-1-4612-6580-1

  • Online ISBN: 978-1-4612-0029-1

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