000			04593nam a22004815i 4500
001			978-1-4614-8024-2
003			DE-He213
005			20140220082831.0
007			cr nn 008mamaa
008			131001s2013 xxu| s |||| 0|eng d
020			_a9781461480242 _9978-1-4614-8024-2
024	7		_a10.1007/978-1-4614-8024-2 _2doi
050		4	_aQA252.3
050		4	_aQA387
072		7	_aPBG _2bicssc
072		7	_aMAT014000 _2bisacsh
072		7	_aMAT038000 _2bisacsh
082	0	4	_a512.55 _223
082	0	4	_a512.482 _223
100	1		_aBump, Daniel. _eauthor.
245	1	0	_aLie Groups _h[electronic resource] / _cby Daniel Bump.
250			_a2nd ed. 2013.
264		1	_aNew York, NY : _bSpringer New York : _bImprint: Springer, _c2013.
300			_aXIII, 551 p. 90 illus. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
490	1		_aGraduate Texts in Mathematics, _x0072-5285 ; _v225
505	0		_aPart I: Compact Topological Groups -- 1 Haar Measure -- 2 Schur Orthogonality -- 3 Compact Operators -- 4 The Peter–Weyl Theorem -- Part II: Compact Lie Groups -- 5 Lie Subgroups of GL(n,C) -- 6 Vector Fields -- 7 Left-Invariant Vector Fields -- 8 The Exponential Map -- 9 Tensors and Universal Properties -- 10 The Universal Enveloping Algebra -- 11 Extension of Scalars -- 12 Representations of sl(2,C) -- 13 The Universal Cover -- 14 The Local Frobenius Theorem -- 15 Tori -- 16 Geodesics and Maximal Tori -- 17 The Weyl Integration Formula -- 18 The Root System -- 19 Examples of Root Systems -- 20 Abstract Weyl Groups -- 21 Highest Weight Vectors -- 22 The Weyl Character Formula -- 23 The Fundamental Group -- Part III: Noncompact Lie Groups -- 24 Complexification -- 25 Coxeter Groups -- 26 The Borel Subgroup.- 27 The Bruhat Decomposition -- 28 Symmetric Spaces.- 29 Relative Root Systems.- 30 Embeddings of Lie Groups -- 31 Spin -- Part IV: Duality and Other Topics -- 32 Mackey Theory -- 33 Characters of GL(n,C) -- 34 Duality between Sk and GL(n,C) -- 35 The Jacobi–Trudi Identity -- 36 Schur Polynomials and GL(n,C) -- 37 Schur Polynomials and Sk.  38 The Cauchy Identity -- 39 Random Matrix Theory -- 40 Symmetric Group Branching Rules and Tableaux -- 41 Unitary Branching Rules and Tableaux -- 42 Minors of Toeplitz Matrices -- 43 The Involution Model for Sk -- 44 Some Symmetric Alegras -- 45 Gelfand Pairs -- 46 Hecke Algebras -- 47 The Philosophy of Cusp Forms.- 48 Cohomology of Grassmannians -- Appendix: Sage -- References -- Index.
520			_aThis book is intended for a one-year graduate course on Lie groups and Lie algebras. The book goes beyond the representation theory of compact Lie groups, which is the basis of many texts, and provides a carefully chosen range of material to give the student the bigger picture. The book is organized to allow different paths through the material depending on one's interests. This second edition has substantial new material, including improved discussions of underlying principles, streamlining of some proofs, and many results and topics that were not in the first edition. For compact Lie groups, the book covers the Peter–Weyl theorem, Lie algebra, conjugacy of maximal tori, the Weyl group, roots and weights, Weyl character formula, the fundamental group and more. The book continues with the study of complex analytic groups and general noncompact Lie groups, covering the Bruhat decomposition, Coxeter groups, flag varieties, symmetric spaces, Satake diagrams, embeddings of Lie groups and spin. Other topics that are treated are symmetric function theory, the representation theory of the symmetric group, Frobenius–Schur duality and GL(n) × GL(m) duality with many applications including some in random matrix theory, branching rules, Toeplitz determinants, combinatorics of tableaux, Gelfand pairs, Hecke algebras, the "philosophy of cusp forms" and the cohomology of Grassmannians. An appendix introduces the reader to the use of Sage mathematical software for Lie group computations.
650		0	_aMathematics.
650		0	_aTopological Groups.
650	1	4	_aMathematics.
650	2	4	_aTopological Groups, Lie Groups.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9781461480235
830		0	_aGraduate Texts in Mathematics, _x0072-5285 ; _v225
856	4	0	_uhttp://dx.doi.org/10.1007/978-1-4614-8024-2
912			_aZDB-2-SMA
999			_c96021 _d96021