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

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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Hlavní autor: Lakshmibai, V. (Autor)
Médium: Elektronický zdroj E-kniha
Jazyk:angličtina
Vydáno: Singapore : Springer Singapore , 2018.
Vydání:2nd ed. 2018.
Edice:Texts and Readings in Mathematics, 53
Témata:
Group theory.
Associative rings.
Rings (Algebra).
Algebraic geometry.
ISBN:9789811313936
ISSN:2366-8717 ;
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Obsah:
  • 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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