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

• Main Authors: Lakshmibai, V. (Author, http://id.loc.gov/vocabulary/relators/aut), Brown, Justin (http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Singapore : Springer Singapore : Imprint: Springer, 2018.
• Edition: 2nd ed. 2018.
• Series: Texts and Readings in Mathematics, 53
• Subjects: Group theory.; Associative rings.; Rings (Algebra).; Algebraic geometry.; Group Theory and Generalizations.; Associative Rings and Algebras.; Algebraic Geometry.

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...

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.