{"product_id":"flag-varieties-an-interplay-of-geometry-combinatorics-and-representation-theory-9789386279705","title":"Flag Varieties: An Interplay of Geometry,","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eFlag varieties are important geometric objects and their study involves an interplay of geometry, combinatorics, and representation theory. This book is a detailed account of this interplay.\u003cbr\u003e\u003cbr\u003eIn the area of representation theory, the book presents a discussion of complex semisimple Lie algebras and of semisimple algebraic groups; in addition, the representation theory of symmetric groups is also discussed. In the area of algebraic geometry, the book gives a detailed account of Grassmann varieties, flag varieties, and their Schubert subvarieties. Because of their connections with root systems, many of the geometric results admit elegant combinatorial description, a typical example being the description of the singular locus of a Schubert variety. This is shown to be a consequence of standard monomial theory (abbreviated SMT). Thus the book includes SMT and some important applications - singular loci of Schubert varieties, toric degenerations of Schubert varieties, and the relationship between Schubert varieties and classical invariant theory.\u003cbr\u003e\u003cbr\u003eIn this second edition, two recent results on Schubert varieties in the Grassmannian have been added, and some errors in the first edition corrected.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cul\u003e\n\u003cli\u003ePreface \u003c\/li\u003e\n\u003cli\u003eIntroduction\u003c\/li\u003e\n\u003cli\u003e1 Preliminaries\u003c\/li\u003e\n\u003cli\u003e2 Structure Theory of Semisimple Rings\u003c\/li\u003e\n\u003cli\u003e3 Representation Theory of Finite Groups\u003c\/li\u003e\n\u003cli\u003e4 Representation Theory of the Symmetric Group\u003c\/li\u003e\n\u003cli\u003e5 Symmetric Polynomials\u003c\/li\u003e\n\u003cli\u003e6 Schur-Weyl Duality and the Relationship Between Representations of Sd and GLn (C)\u003c\/li\u003e\n\u003cli\u003e7 Structure Theory of Complex Semisimple Lie Algebras\u003c\/li\u003e\n\u003cli\u003e8 Representation Theory of Complex Semisimple Lie Algebras\u003c\/li\u003e\n\u003cli\u003e9 Generalities on Algebraic Groups\u003c\/li\u003e\n\u003cli\u003e10 Structure Theory of Reductive Groups\u003c\/li\u003e\n\u003cli\u003e11 Representation Theory of Semisimple Algebraic Groups\u003c\/li\u003e\n\u003cli\u003e12 Geometry of the Grassmannian, Flag and their Schubert Varieties via Standard Monomial Theory\u003c\/li\u003e\n\u003cli\u003e13 Singular Locus of a Schubert Variety in the Flag Variety SLn \/ B \u003c\/li\u003e\n\u003cli\u003e14 Applications\u003c\/li\u003e\n\u003cli\u003e15 Free Resolutions of Some Schubert Singularities\u003c\/li\u003e\n\u003cli\u003e16 Levi Subgroup Actions on Schubert Varieties, and Some Geometric\u003c\/li\u003e\n\u003cli\u003eConsequences\u003c\/li\u003e\n\u003cli\u003eAppendix A: Chevalley Groups\u003c\/li\u003e\n\u003cli\u003eReferences\u003c\/li\u003e\n\u003cli\u003eList of Symbols\u003c\/li\u003e\n\u003cli\u003eIndex\u003c\/li\u003e\n\u003c\/ul\u003e","brand":"Jainendra K Jain","offers":[{"title":"Default Title","offer_id":50473223061847,"sku":"9789386279705","price":52.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9789386279705.jpg?v=1744905769","url":"https:\/\/bookcurl.com\/products\/flag-varieties-an-interplay-of-geometry-combinatorics-and-representation-theory-9789386279705","provider":"Book Curl","version":"1.0","type":"link"}