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The Resource Flag Varieties : An Interplay of Geometry, Combinatorics, and Representation Theory, by V. Lakshmibai, Justin Brown, (electronic resource)
Flag Varieties : An Interplay of Geometry, Combinatorics, and Representation Theory, by V. Lakshmibai, Justin Brown, (electronic resource)
Resource Information
The item Flag Varieties : An Interplay of Geometry, Combinatorics, and Representation Theory, by V. Lakshmibai, Justin Brown, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Manitoba Libraries.This item is available to borrow from all library branches.
Resource Information
The item Flag Varieties : An Interplay of Geometry, Combinatorics, and Representation Theory, by V. Lakshmibai, Justin Brown, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Manitoba Libraries.
This item is available to borrow from all library branches.
 Summary
 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 representationtheoretic consequences
 Language
 eng
 Edition
 Second edition.
 Extent
 1 online resource (xiv, 312 pages).
 Contents

 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. SchurWeyl 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
 Isbn
 9789811313936
 Label
 Flag Varieties : An Interplay of Geometry, Combinatorics, and Representation Theory
 Title
 Flag Varieties
 Title remainder
 An Interplay of Geometry, Combinatorics, and Representation Theory
 Statement of responsibility
 by V. Lakshmibai, Justin Brown
 Language
 eng
 Summary
 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 representationtheoretic consequences
 Cataloging source
 MiAaPQ
 http://library.link/vocab/creatorName
 Lakshmibai, V
 Dewey number
 516.35
 LC call number
 QA174183
 Literary form
 non fiction
 Nature of contents
 dictionaries
 http://library.link/vocab/relatedWorkOrContributorName
 Brown, Justin.
 Series statement
 Texts and Readings in Mathematics,
 Series volume
 53
 http://library.link/vocab/subjectName

 Mathematics
 Algebraic geometry
 Associative rings
 Rings (Algebra)
 Group theory
 Mathematics
 Group Theory and Generalizations
 Associative Rings and Algebras
 Algebraic Geometry
 Label
 Flag Varieties : An Interplay of Geometry, Combinatorics, and Representation Theory, by V. Lakshmibai, Justin Brown, (electronic resource)
 Carrier category
 online resource
 Carrier category code
 cr
 Carrier MARC source
 rdacarrier
 Color
 multicolored
 Content category
 text
 Content type code
 txt
 Content type MARC source
 rdacontent
 Contents
 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. SchurWeyl 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
 Dimensions
 unknown
 Edition
 Second edition.
 Extent
 1 online resource (xiv, 312 pages).
 Form of item
 online
 Isbn
 9789811313936
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code
 c
 Other control number
 10.1007/9789811313936
 Sound
 unknown sound
 Specific material designation
 remote
 System control number

 (CKB)4100000004974923
 (MiAaPQ)EBC5438642
 (DEHe213)9789811313936
 (EXLCZ)994100000004974923
 Label
 Flag Varieties : An Interplay of Geometry, Combinatorics, and Representation Theory, by V. Lakshmibai, Justin Brown, (electronic resource)
 Carrier category
 online resource
 Carrier category code
 cr
 Carrier MARC source
 rdacarrier
 Color
 multicolored
 Content category
 text
 Content type code
 txt
 Content type MARC source
 rdacontent
 Contents
 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. SchurWeyl 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
 Dimensions
 unknown
 Edition
 Second edition.
 Extent
 1 online resource (xiv, 312 pages).
 Form of item
 online
 Isbn
 9789811313936
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code
 c
 Other control number
 10.1007/9789811313936
 Sound
 unknown sound
 Specific material designation
 remote
 System control number

 (CKB)4100000004974923
 (MiAaPQ)EBC5438642
 (DEHe213)9789811313936
 (EXLCZ)994100000004974923
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<div class="citation" vocab="http://schema.org/"><i class="fa faexternallinksquare fafw"></i> Data from <span resource="http://link.lib.umanitoba.ca/portal/FlagVarietiesAnInterplayofGeometry/xQ48qjHIXTc/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.lib.umanitoba.ca/portal/FlagVarietiesAnInterplayofGeometry/xQ48qjHIXTc/">Flag Varieties : An Interplay of Geometry, Combinatorics, and Representation Theory, by V. Lakshmibai, Justin Brown, (electronic resource)</a></span>  <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.lib.umanitoba.ca/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.lib.umanitoba.ca/">University of Manitoba Libraries</a></span></span></span></span></div>