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Spherical Inversion on Sln

Spherical Inversion on Sln


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About the Book

Harish-Chandra s general Plancherel inversion theorem admits a much shorter presentation for spherical functions. Previous expositions have dealt with a general, wide class of Lie groups. This has made access to the subject difficult for outsiders, who may wish to connect some aspects with several if not all other parts of mathematics. In this book, the essential features of Harish-Chandra theory are exhibited on SLn(R), but hundreds of pages of background are replaced by short direct verifications. The material is accessible to graduate students with no background in Lie groups and representation theory.

Review :
From the reviews: "[This] book presents the essential features of the theory on SLn(R). This makes the book accessible to a wide class of readers, including nonexperts of Lie groups and representation theory and outsiders who would like to see connections of some aspects with other parts of mathematics. This feature is widely to be appreciated, together with the clearness of exposition and the way the book is structured." -Sergio Console, Zentralblatt "This book is devoted to Harish-Chandra s Plancherel inversion formula in the special case of the group SLn(R) and for spherical functions. ... the book is easily accessible and essentially self contained." (A. Cap, Monatshefte fur Mathematik, Vol. 140 (2), 2003) "Roughly, this book offers a functorial exposition of the theory of spherical functions developed in the late 1950s by Harish-Chandra, who never used the word functor . More seriously, the authors make a considerable effort to communicate the theory to an outsider . .... However, even an expert will notice several new and pleasing results like the smooth version of the Chevally restriction theorem in Chapter 1." (Tomasz Przebinda, Mathematical Reviews, Issue 2002 j) "This excellent book is an original presentation of Harish-Chandra s general results ... . Unlike previous expositions which dealt with general Lie groups, the present book presents the essential features of the theory on SLn(R). This makes the book accessible to a wide class of readers, including nonexperts ... . This feature is widely to be appreciated, together with the clearness of exposition and the way the book is structured. Very nice is, for instance, the ... table of the decompositions of Lie groups." (Sergio Console, Zentralblatt MATH, Vol. 973, 2001)


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Product Details
  • ISBN-13: 9781468493030
  • Publisher: Springer My Copy UK
  • Publisher Imprint: Springer My Copy UK
  • Height: 234 mm
  • Weight: 621 gr
  • ISBN-10: 1468493035
  • Publisher Date: 21 Jun 2001
  • Binding: Paperback
  • Spine Width: 23 mm
  • Width: 156 mm


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