000 03063nam a22004815i 4500
001 978-3-8348-9401-4
003 DE-He213
005 20161121231133.0
007 cr nn 008mamaa
008 100301s2007 gw | s |||| 0|eng d
020 _a9783834894014
_9978-3-8348-9401-4
024 7 _a10.1007/978-3-8348-9401-4
_2doi
050 4 _aQA184-205
072 7 _aPBF
_2bicssc
072 7 _aMAT002050
_2bisacsh
082 0 4 _a512.5
_223
100 1 _aBerndt, Rolf.
_eauthor.
245 1 0 _aRepresentations of Linear Groups
_h[electronic resource] :
_bAn Introduction Based on Examples from Physics and Number Theory /
_cby Rolf Berndt.
264 1 _aWiesbaden :
_bVieweg,
_c2007.
300 _aXII, 271 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
505 0 _aPrologue: Some Groups and their Actions -- Basic Algebraic Concepts for Group Representations -- Representations of Finite Groups -- Continuous Representations -- Representations of Compact Groups -- Representations of Abelian Groups -- The Infinitesimal Method -- Induced Representations -- Geometric Quantization and the Orbit Method -- Epilogue: Outlook to Number Theory.
520 _aThis is an elementary introduction to the representation theory of real and complex matrix groups. The text is written for students in mathematics and physics who have a good knowledge of differential/integral calculus and linear algebra and are familiar with basic facts from algebra, number theory and complex analysis. The goal is to present the fundamental concepts of representation theory, to describe the connection between them, and to explain some of their background. The focus is on groups which are of particular interest for applications in physics and number theory (e.g. Gell-Mann's eightfold way and theta functions, automorphic forms). The reader finds a large variety of examples which are presented in detail and from different points of view. The examples motivate the general theory well covered already by the existing literature. Hence for complete proofs of most of the essential statements and theorems the reader is often referred to the standard sources. Plenty of exercises are included in the text. Some of these exercises and/or omitted proofs may give a starting point for a bachelor thesis and further studies in a master program.
650 0 _aMathematics.
650 0 _aAlgebra.
650 0 _aGroup theory.
650 0 _aMatrix theory.
650 0 _aNumber theory.
650 1 4 _aMathematics.
650 2 4 _aLinear and Multilinear Algebras, Matrix Theory.
650 2 4 _aAlgebra.
650 2 4 _aNumber Theory.
650 2 4 _aGroup Theory and Generalizations.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783834803191
856 4 0 _uhttp://dx.doi.org/10.1007/978-3-8348-9401-4
912 _aZDB-2-SMA
950 _aMathematics and Statistics (Springer-11649)
999 _c509122
_d509122