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000843799 019__ $$a1043409423
000843799 020__ $$a9789811313936$$q(electronic book)
000843799 020__ $$a9811313938$$q(electronic book)
000843799 0247_ $$a10.1007/978-981-13-1393-6$$2doi
000843799 035__ $$aSP(OCoLC)on1042331376
000843799 035__ $$aSP(OCoLC)1042331376$$z(OCoLC)1043409423
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000843799 049__ $$aISEA
000843799 050_4 $$aQA564
000843799 08204 $$a516.353$$223
000843799 1001_ $$aLakshmibai, V.$$q(Venkatramani),$$eauthor.
000843799 24510 $$aFlag varieties :$$ban interplay of geometry, combinatorics, and representation theory /$$cV. Lakshmibai, Justin Brown.
000843799 250__ $$aSecond edition.
000843799 264_1 $$aSingapore :$$bSpringer,$$c2018.
000843799 300__ $$a1 online resource (xiv, 312 pages) :$$billustrations.
000843799 336__ $$atext$$btxt$$2rdacontent
000843799 337__ $$acomputer$$bc$$2rdamedia
000843799 338__ $$aonline resource$$bcr$$2rdacarrier
000843799 4901_ $$aTexts and readings in mathematics,$$x2366-8717 ;$$vvolume 53
000843799 504__ $$aIncludes bibliographical references and index.
000843799 5050_ $$aIntro; Preface; Contents; About the Authors; Introduction; 1 Preliminaries; 1.1 Commutative Algebra; 1.2 Affine Varieties; 1.3 Projective Varieties; 1.4 Schemes -- Affine and Projective; 1.5 The Scheme Spec(A); 1.6 The Scheme Proj(S); 1.7 Sheaves of OX-Modules; 1.8 Attributes of Varieties; 2 Structure Theory of Semisimple Rings; 2.1 Semisimple Modules; 2.2 Semisimple Rings; 2.3 Brauer Groups and Central Simple Algebras; 2.4 The Group Algebra, K[G]; 2.5 The Center of K[G]; Exercises; 3 Representation Theory of Finite Groups; 3.1 Representations of G; 3.2 Characters of Representations
000843799 5058_ $$a6 Schur-Weyl Duality and the Relationship Between Representations of Sd and GLn (C)6.1 Generalities; 6.2 Schur-Weyl Duality; 6.3 Characters of the Schur Modules; 6.4 Schur Module Representations of SLn (C); 6.5 Representations of GLn (C); Exercises; 7 Structure Theory of Complex Semisimple Lie Algebras; 7.1 Introduction to Semisimple Lie Algebras; 7.2 The Exponential Map in Characteristic Zero; 7.3 Structure of Semisimple Lie Algebras; 7.4 Jordan Decomposition in Semisimple Lie Algebras; 7.5 The Lie Algebra sln (C); 7.6 Cartan Subalgebras; 7.7 Root Systems; 7.8 Structure Theory of sln (C)
000843799 5058_ $$aExercises8 Representation Theory of Complex Semisimple Lie Algebras; 8.1 Representations of g; 8.2 Weight Spaces; 8.3 Finite Dimensional Modules; 8.4 Fundamental Weights; 8.5 Dimension and Character Formulas; 8.6 Irreducible sln (C)-Modules; Exercises; 9 Generalities on Algebraic Groups; 9.1 Algebraic Groups and Their Lie Algebras; 9.2 The Tangent Space; 9.3 Jordan Decomposition in G; 9.4 Variety Structure on G/H; 9.5 The Flag Variety; 9.6 Structure of Connected Solvable Groups; 9.7 Borel Fixed Point Theorem; 9.8 Variety of Borel Subgroups; Exercises; 10 Structure Theory of Reductive Groups
000843799 506__ $$aAccess limited to authorized users.
000843799 520__ $$aThis book discusses the importance of flag varieties in geometric objects and elucidates its richness as interplay of geometry, combinatorics and representation theory. The book presents a discussion on the representation theory of complex semisimple Lie algebras, as well as the representation theory of semisimple algebraic groups. In addition, the book also discusses the representation theory of symmetric groups. In the area of algebraic geometry, the book gives a detailed account of the Grassmannian varieties, flag varieties, and their Schubert subvarieties. Many of the geometric results admit elegant combinatorial description because of the root system connections, a typical example being the description of the singular locus of a Schubert variety. This discussion is carried out as a consequence of standard monomial theory. Consequently, this book includes standard monomial theory and some important applications—singular loci of Schubert varieties, toric degenerations of Schubert varieties, and the relationship between Schubert varieties and classical invariant theory. The two recent results on Schubert varieties in the Grassmannian have also been included in this book. The first result gives a free resolution of certain Schubert singularities. The second result is about certain Levi subgroup actions on Schubert varieties in the Grassmannian and derives some interesting geometric and representation-theoretic consequences.--$$cProvided by publisher.
000843799 588__ $$aOnline resource; title from PDF title page (SpringerLink, viewed July 2, 2018).
000843799 650_0 $$aGeometry, Algebraic.
000843799 650_0 $$aFlag manifolds.
000843799 650_0 $$aRepresentations of groups.
000843799 650_0 $$aSemisimple Lie groups.
000843799 650_0 $$aSchubert varieties.
000843799 7001_ $$aBrown, Justin$$q(Justin Allen),$$eauthor.
000843799 830_0 $$aTexts and readings in mathematics ;$$v53.
000843799 852__ $$bebk
000843799 85640 $$3SpringerLink$$uhttps://univsouthin.idm.oclc.org/login?url=http://link.springer.com/10.1007/978-981-13-1393-6$$zOnline Access$$91397441.1
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