國立高雄大學圖資館 |

Language: English

Back

Flag varietiesan interplay of geomet...

Brown, Justin.

Flag varietiesan interplay of geometry, combinatorics, and representation theory /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Flag varietiesby 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$q(electronic bk.)

Flag varietiesan 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 ;74..

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$q(electronic bk.)

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

190843
Geometry, Algebraic.

LC Class. No.: QA564 / .L357 2018

Dewey Class. No.: 516.353

Flag varietiesan interplay of geometry, combinatorics, and representation theory /
LDR:03489nmm a2200325 a 4500 001 540779
003 DE-He213
005 20190110114015.0
006 m d
007 cr nn 008maaau
008 190308s2018 si s 0 eng d
020 $a 9789811313936$q(electronic bk.)
024 7 $a 10.1007/978-981-13-1393-6 $2 doi
035 $a 978-981-13-1393-6
040 $a GP $c GP
041 0 $a eng
050 4 $a QA564 $b .L357 2018
072 7 $a PBG $2 bicssc
072 7 $a MAT002010 $2 bisacsh
082 0 4 $a 516.353 $2 23
090 $a QA564 $b .L192 2018
100 1 $a Lakshmibai, V. $3 731677
245 1 0 $a Flag varieties $h [electronic resource] : $b an interplay of geometry, combinatorics, and representation theory / $c by V. Lakshmibai, Justin Brown.
250 $a 2nd ed.
260 $a Singapore : $b Springer Singapore : $b Imprint: Springer, $c 2018.
300 $a xiv, 312 p. : $b ill., digital ; $c 24 cm.
490 1 $a Texts and readings in mathematics, $x 2366-8717 ; $v v.53
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 190843
650 0 $a Flag manifolds. $3 497826
650 0 $a Representations of groups. $3 191076
650 0 $a Semisimple Lie groups. $3 819231
650 0 $a Schubert varieties. $3 275771
650 1 4 $a Mathematics. $3 184409
650 2 4 $a Group Theory and Generalizations. $3 274819
650 2 4 $a Associative Rings and Algebras. $3 274818
650 2 4 $a Algebraic Geometry. $3 274807
700 1 $a Brown, Justin. $3 731678
710 2 $a SpringerLink (Online service) $3 273601
773 0 $t Springer eBooks
830 0 $a Texts and readings in mathematics ; $v 74. $3 789679
856 4 0 $u http://dx.doi.org/10.1007/978-981-13-1393-6
950 $a Mathematics and Statistics (Springer-11649)