Buildings and Classical Groups PDF
By:Paul B. Garrett
Published on 1997-04-01 by CRC Press
Buildings are highly structured, geometric objects, primarily used in the finer study of the groups that act upon them. In Buildings and Classical Groups, the author develops the basic theory of buildings and BN-pairs, with a focus on the results needed to apply it to the representation theory of p-adic groups. In particular, he addresses spherical and affine buildings, and the |spherical building at infinity| attached to an affine building. He also covers in detail many otherwise apocryphal results. Classical matrix groups play a prominent role in this study, not only as vehicles to illustrate general results but as primary objects of interest. The author introduces and completely develops terminology and results relevant to classical groups. He also emphasizes the importance of the reflection, or Coxeter groups and develops from scratch everything about reflection groups needed for this study of buildings. In addressing the more elementary spherical constructions, the background pertaining to classical groups includes basic results about quadratic forms, alternating forms, and hermitian forms on vector spaces, plus a description of parabolic subgroups as stabilizers of flags of subspaces. The text then moves on to a detailed study of the subtler, less commonly treated affine case, where the background concerns p-adic numbers, more general discrete valuation rings, and lattices in vector spaces over ultrametric fields. Buildings and Classical Groups provides essential background material for specialists in several fields, particularly mathematicians interested in automorphic forms, representation theory, p-adic groups, number theory, algebraic groups, and Lie theory. No other available source provides such a complete and detailed treatment.
This Book was ranked at 40 by Google Books for keyword Buildings.
Book ID of Buildings and Classical Groups's Books is OFGMPwnTUq8C, Book which was written byPaul B. Garretthave ETAG "U19UYoMaR4c"
Book which was published by CRC Press since 1997-04-01 have ISBNs, ISBN 13 Code is 9780412063312 and ISBN 10 Code is 041206331X
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Book which have "416 Pages" is Printed at BOOK under CategoryMathematics
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