Standard Monomial Theory : Invariant Theoretic Approach

V. Lakshmibai

ISBN 10: 3540767568 / ISBN 13: 9783540767565

Edité par Springer, Springer Vieweg, 2008

A propos de cet article

Druck auf Anfrage Neuware - Printed after ordering - Schubert varieties lie at the cross roads of algebraic geometry, combinatorics, commutative algebra, and representation theory. They are an important class of subvarieties of flag varieties, interesting in their own right, and providing an inductive tool for studying flag varieties. The literature on them is vast, for they are ubiquitous - they have been intensively studied over the last fifty years, from many different points of view.This book is mainly a detailed account of a particularly interesting instance of their occurrence: namely, in relation to classical invariant theory. More precisely, it is about the connection between the first and second fundamental theorems of classical invariant theory and standard monomial theory for Schubert varieties in certain special flag varieties. Historically, this connection was the prime motivation for the development of standard monomial theory. Determinantal varieties and basic concepts of geometric invariant theory arise naturally in establishing the connection.

N° de réf. du vendeur 9783540767565

Détails bibliographiques

• Titre: Standard Monomial Theory : Invariant Theoretic Approach
• Éditeur: Springer, Springer Vieweg
• Date de parution: 2008
• Langue: anglais
• ISBN à 10 chiffres: 3540767568
• ISBN à 13 chiffres: 9783540767565
• Reliure: Buch
• État de l'article: Neu
• Dimensions: 241 L x 160 H x 20 P (en millimètres) 241 millimètres de largeur par 160 millimètres de hauteur par 20 millimètres de profondeur
• Poids: 588 grammes

A propos de ce titre

Synopsis

Schubert varieties lie at the cross roads of algebraic geometry, combinatorics, commutative algebra, and representation theory. They are an important class of subvarieties of flag varieties, interesting in their own right, and providing an inductive tool for studying flag varieties. The literature on them is vast, for they are ubiquitous - they have been intensively studied over the last fifty years, from many different points of view.

This book is mainly a detailed account of a particularly interesting instance of their occurrence: namely, in relation to classical invariant theory. More precisely, it is about the connection between the first and second fundamental theorems of classical invariant theory and standard monomial theory for Schubert varieties in certain special flag varieties. Historically, this connection was the prime motivation for the development of standard monomial theory. Determinantal varieties and basic concepts of geometric invariant theory arise naturally in establishing the connection.

Présentation de l'éditeur

Schubert varieties provide an inductive tool for studying flag varieties. This book is mainly a detailed account of a particularly interesting instance of their occurrence: namely, in relation to classical invariant theory. More precisely, it is about the connection between the first and second fundamental theorems of classical invariant theory on the one hand and standard monomial theory for Schubert varieties in certain special flag varieties on the other.