Flag Varieties An Interplay of Geometry, Combinatorics, and Representation Theory

Flag Varieties An Interplay of Geometry, Combinatorics, and Representation Theory / by V Lakshmibai, Justin Brown.

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 theor...

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Bibliographic Details
Main Authors: Lakshmibai, V. (Author), Brown, Justin (Author)
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: Singapore : Springer Singapore : Imprint: Springer, 2018.
Edition:2nd ed. 2018.
Series:Texts and Readings in Mathematics, 53
Springer eBook Collection.
Subjects:
Group theory.
Associative rings.
Rings (Algebra).
Algebraic geometry.
Electronic resources (E-books)
Online Access:Click to view e-book
Holy Cross Note:Loaded electronically.
Electronic access restricted to members of the Holy Cross Community.
Table of 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. 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.

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