000			04415nam a2200385 i 4500
001			19999
005			20260309163726.0
008			040715t20042004nyua b 001 0 eng d
020			_a0387211543 _q(hard : alk. paper)
020			_a9780387211541 _q(hard : alk. paper)
020			_a1441919376
020			_a9781441919373
035			_a(OCoLC)55739480 _z(OCoLC)56655861 _z(OCoLC)723108139
040			_aMIA _beng _cMIA _dDLC _dOHX _dBAKER _dNLGGC _dBTCTA _dLVB _dYDXCP _dUBA _dUKM _dOCLCG _dHEBIS _dUKMGB _dMNW _dOCLCO _dMUU _dOCLCF _dDEBSZ _dP4I _dOCLCQ _dUtOrBLW _dBAUN
041	0		_aeng
049			_aBAUN_MERKEZ
050	0	4	_aQA387 _b.B76 2004
082	0	0	_222
100	1		_aBump, Daniel, _d1952- _978326 _eaut
245	1	0	_aLie groups / _cDaniel Bump
264		1	_aNew York : _bSpringer, _c[2004]
264		4	_c©2004
300			_axi, 451 pages : _billustrations ; _c24 cm
336			_atext _btxt _2rdacontent
337			_aunmediated _bn _2rdamedia
338			_avolume _bnc _2rdacarrier
490	1		_aGraduate texts in mathematics ; _v225
504			_aIncludes bibliographical references (pages 438-445) and index
505	0	0	_tpt. I: Compact groups. Haar measure _t-- Schur orthogonality _t-- Compact operators _t-- The Peter-Weyl theorem _t-- part II: Lie groups fundamentals. Lie subgroups of GL (n, C) _t-- Vector fields _t-- Left-invariant vector fields _t-- The exponential map _t-- Tensors and universal properties _t-- The universal enveloping algebra _t-- Extension of scalars _t-- Representations of s1(2,C) _t-- The universal cover _t-- The local Frobenius theorem _t-- Tori _t-- Geodesics and maximal tori _t-- Topological proof of Cartan's theorem _t-- The Weyl integration formula _t-- The root system _t-- Examples of root systems _t-- Abstract Weyl groups _t-- The fundamental group _t-- Semisimple compact groups _t-- Highest-Weight vectors _t-- The Weyl character formula _t-- Spin _t-- Complexification _t-- Coxeter groups _t-- The Iwasawa decomposition _t-- The Bruhat decomposition _t-- Symmetric spaces _t-- Relative root systems _t-- Embeddings of lie groups _t-- part III: Topics. Mackey theory _t-- Characters of GL(n, C) _t-- Duality between Sk and GL(n, C) _t-- The Jacobi-Trudi identity _t-- Schur polynomials and GL(n, C) _t-- Schur polynomials and Sk _t-- Random matrix theory _t-- Minors of Toeplitz matrices _t-- Branching formulae and tableaux _t-- The Cauchy identity _t-- Unitary branching rules _t-- The involution model for Sk _t-- Some symmetric algebras _t-- Gelfand pairs _t-- Hecke algebras _t-- The philosophy of cusp forms _t-- Cohomology of Grassmannians
520			_a"This book is intended for a one year graduate course on Lie groups and Lie algebras. The author proceeds 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. For compact Lie groups, the Peter-Weyl theorem, conjugacy of maximal tori (two proofs), Weyl character formula and more are covered. The book continues with the study of complex analytic groups, then general noncompact Lie groups, including the Coxeter presentation of the Weyl group, the Iwasawa and Bruhat decompositions, Cartan decomposition, symmetric spaces, Cayley transforms, relative root systems, Satake diagrams, extended Dynkin diagrams and a survey of the ways Lie groups may be embedded in one another. The book culminates in a "topics" section giving depth to the student's understanding of representation theory, taking the Frobenius-Schur duality between the representation theory of the symmetric group and the unitary groups as a unifying theme, with many applications in diverse areas such as random matrix theory, minors of Toeplitz matrices, symmetric algebra decompositions, Gelfand pairs, Hecke algebras, representations of finite general linear groups and the cohomology of Grassmannians and flag varieties. Daniel Bump is Professor of Mathematics at Stanford University. His research is in automorphic forms, representation theory and number theory. He is a co-author of GNU Go, a computer program that plays the game of Go. His previous books include Automorphic Forms and Representations (Cambridge University Press 1997) and Algebraic Geometry (World Scientific 1998)."--Publisher's website
650		0	_aLie groups _978327
830		0	_919347 _aGraduate texts in mathematics ; _v225
900			_bSatın
942			_2lcc _cKT
999			_c16832 _d16832