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020			_a9788181284495
035			_a(OCoLC)ocn861337404
040			_aIISER Bhopal _beng _cVBD
042			_alccopycat
050	0	0	_aQA387 _b.B76 2013
082	0	0	_a512.482 B88L _223
100	1		_aBump, Daniel. _96141
222			_aMathematics Collection
245	1	0	_aLie groups _cDaniel Bump.
260			_aNew Delhi : _bSpringer, _c2004.
300			_axiii, 551 p. : _bill. ; _c25 cm.
440			_aGraduate text in mathematics; _n225 _99646
504			_aIncludes bibliographical references (pages 535-544) and index.
505	0	0	_gPt. I: _tCompact groups. _tHaar measure -- _tSchur orthogonality -- _tCompact operators -- _tThe Peter-Weyl theorem -- _gpt. II: _tLie groups fundamentals. _tLie subgroups of GL (n,C) -- _tVector fields -- _tLeft-invariant vector fields -- _tThe exponential map -- _tTensors and universal properties -- _tThe universal enveloping algebra -- _tExtension of scalars -- _tRepresentations of s1(2,C) -- _tThe universal cover -- _tThe local Frobenius theorem -- _tTori -- _tGeodesics and maximal tori -- _tTopological proof of Cartan's theorem -- _tThe Weyl integration formula -- _tThe root system -- _tExamples of root systems -- _tAbstract Weyl groups -- _tThe fundamental group -- _tSemisimple compact groups -- _tHighest-Weight vectors -- _tThe Weyl character formula -- _tSpin -- _tComplexification -- _tCoxeter groups -- _tThe Iwasawa decomposition -- _tThe Bruhat decomposition -- _tSymmetric spaces -- _tRelative root systems -- _tEmbeddings of lie groups -- _gpt. III: _tTopics. _tMackey theory -- _tCharacters of GL(n,C) -- _tDuality between Sk and GL(n, C) -- _tThe Jacobi-Trudi identity -- _tSchur polynomials and GL(n,C) -- _tSchur polynomials and Sk -- _tRandom matrix theory -- _tMinors of Toeplitz matrices -- _tBranching formulae and tableaux -- _tThe Cauchy identity -- _tUnitary branching rules -- _tThe involution model for Sk -- _tSome symmetric algebras -- _tGelfand pairs -- _tHecke algebras -- _tThe philosophy of cusp forms -- _tCohomology 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.--
650		0	_aLie groups. _96142
650		0	_aMathematics. _96143
830		0	_aGraduate texts in mathematics ; _v225. _96144
906			_a7 _bcbc _ccopycat _d2 _encip _f20 _gy-gencatlg
942			_2ddc _cBK
999			_c5994 _d5994