Flag Varieties

An Interplay of Geometry, Combinatorics, and Representation Theory

V. Lakshmibai (Autor)

Buch | Hardcover

286 Seiten

2009
Hindustan Book Agency (Verlag)
978-81-85931-92-0 (ISBN)

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Flag varieties are important geometric objects and their study involves an interplay of geometry, combinatorics, and representation theory. This book is detailed account of this interplay. In the area of representation theory, the book presents a discussion of complex semisimple Lie algebras and of semisimple algebraic groups; in addition, the representation theory of symmetric groups is also discussed. In the area of algebraic geometry, the book gives a detailed account of the Grassmannian varieties, flag varieties, and their Schubert subvarieties. Because of the connections with root systems, many of the geometric results admit elegant combinatorial description, a typical example being the description of the singular locus of a Schubert variety. This is shown to be a consequence of standard monomial theory (abbreviated SMT). Thus the book includes SMT and some important applications - singular loci of Schubert varieties, toric degenerations of Schubert varieties, and the relationship between Schubert varieties and classical invariant theory.

Introduction.; 1. Preliminaries; 2. Structure Theory of Semisimple Rings; 3. Representation Theory of Finite Groups; 4. Representation Theory of the Symmetric Group; 5. Symmetric Polynomials; 6. Schur-Weyl Duality and the Relationship Between Representations of Sd and GLn (C); 7. Structure Theory of Complex Semisimple Lie Algebras; 8. Representation Theory of Complex Semisimple Lie Algebras; 9. Generalities on Algebraic Groups; 10. Structure Theory of Reductive Groups; 11. Representation Theory of Semisimple Algebraic Groups; 12. Geometry of the Grassmannian, Flag and their Schubert Varieties via Standard Monomial Theory; 13. Singular Locus of a Schubert Variety in the Flag Variety SLn/B; 14. Applications.; Appendix: Chevalley Groups.; Bibliography.; List of Symbols.; Index.

Erscheint lt. Verlag	15.1.2009
Reihe/Serie	Texts and Readings in Mathematics ; 53
Zusatzinfo	286 p.
Verlagsort	New Delhi
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
Themenwelt	Mathematik / Informatik ► Mathematik ► Graphentheorie
ISBN-10	81-85931-92-5 / 8185931925
ISBN-13	978-81-85931-92-0 / 9788185931920
Zustand	Neuware