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Flag varieties = an interplay of geometry, combinatorics, and representation theory /

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Flag varieties/ by V. Lakshmibai, Justin Brown.
Reminder of title:	an interplay of geometry, combinatorics, and representation theory /
Author:	Lakshmibai, V.
other author:	Brown, Justin.
Published:	Singapore :Springer Singapore : : 2018.,
Description:	xiv, 312 p. :ill., digital ; : 24 cm.;
Contained By:	Springer eBooks
Subject:	Geometry, Algebraic. -
Online resource:	http://dx.doi.org/10.1007/978-981-13-1393-6
ISBN:	9789811313936

Flag varieties = an interplay of geometry, combinatorics, and representation theory /
Lakshmibai, V.

Flag varietiesan interplay of geometry, combinatorics, and representation theory /[electronic resource] :by V. Lakshmibai, Justin Brown. - 2nd ed. - Singapore :Springer Singapore :2018. - xiv, 312 p. :ill., digital ;24 cm. - Texts and readings in mathematics,v.532366-8717 ;. - Texts and readings in mathematics ;37-38..

Chapter 1. Preliminaries -- Chapter 2. Structure Theory of Semisimple Rings -- Chapter 3. Representation Theory of Finite Groups -- Chapter 4. Representation Theory of the Symmetric Group -- Chapter 5. Symmetric Polynomials -- Chapter 6. Schur-Weyl Duality and the Relationship Between Representations of Sd and GLn (C) -- Chapter 7. Structure Theory of Complex Semisimple Lie Algebras -- Chapter 8. Representation Theory of Complex Semisimple Lie Algebras -- Chapter 9. Generalities on Algebraic Groups -- Chapter 10. Structure Theory of Reductive Groups -- Chapter 11. Representation Theory of Semisimple Algebraic Groups -- Chapter 12. Geometry of the Grassmannian, Flag and their Schubert Varieties via Standard Monomial Theory -- Chapter 13. Singular Locus of a Schubert Variety in the Flag Variety SLn=B -- Chapter 14. Applications -- Chapter 15. Free Resolutions of Some Schubert Singularities -- Chapter 16. Levi Subgroup Actions on Schubert Varieties, and Some Geometric Consequences.

This 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.

ISBN: 9789811313936

Standard No.: 10.1007/978-981-13-1393-6doiSubjects--Topical Terms:

580393
Geometry, Algebraic.

LC Class. No.: QA564 / .L357 2018

Dewey Class. No.: 516.353

Flag varieties = an interplay of geometry, combinatorics, and representation theory /
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505 0 $a Chapter 1. Preliminaries -- Chapter 2. Structure Theory of Semisimple Rings -- Chapter 3. Representation Theory of Finite Groups -- Chapter 4. Representation Theory of the Symmetric Group -- Chapter 5. Symmetric Polynomials -- Chapter 6. Schur-Weyl Duality and the Relationship Between Representations of Sd and GLn (C) -- Chapter 7. Structure Theory of Complex Semisimple Lie Algebras -- Chapter 8. Representation Theory of Complex Semisimple Lie Algebras -- Chapter 9. Generalities on Algebraic Groups -- Chapter 10. Structure Theory of Reductive Groups -- Chapter 11. Representation Theory of Semisimple Algebraic Groups -- Chapter 12. Geometry of the Grassmannian, Flag and their Schubert Varieties via Standard Monomial Theory -- Chapter 13. Singular Locus of a Schubert Variety in the Flag Variety SLn=B -- Chapter 14. Applications -- Chapter 15. Free Resolutions of Some Schubert Singularities -- Chapter 16. Levi Subgroup Actions on Schubert Varieties, and Some Geometric Consequences.
520 $a This 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.
650 0 $a Geometry, Algebraic. $3 580393
650 0 $a Flag manifolds. $3 1206437
650 0 $a Representations of groups. $3 672181
650 0 $a Semisimple Lie groups. $3 1206438
650 0 $a Schubert varieties. $3 678228
650 1 4 $a Mathematics. $3 527692
650 2 4 $a Group Theory and Generalizations. $3 672112
650 2 4 $a Associative Rings and Algebras. $3 672306
650 2 4 $a Algebraic Geometry. $3 670184
700 1 $a Brown, Justin. $3 1069781
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950 $a Mathematics and Statistics (Springer-11649)