Téléchargez le livre : Flag Varieties

Flag Varieties

An Interplay of Geometry, Combinatorics, and Representation Theory de

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Éditeur :

Springer


Collection :

Texts and Readings in Mathematics

Paru le : 2018-06-26

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Description


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 representation-theoretic consequences.
Pages
312 pages
Collection
Texts and Readings in Mathematics
Parution
2018-06-26
Marque
Springer
EAN papier
9789811313936
EAN PDF
9789811313936
Informations sur l'ebook
Nombre pages copiables
3
Nombre pages imprimables
31
Taille du fichier
2877 Ko
Prix
116,04 €

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