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Standard Monomial Theory

Invariant Theoretic Approach
BuchKartoniert, Paperback
266 Seiten
Englisch
Springererschienen am22.11.2010Softcover reprint of hardcover 1st ed. 2008
Schubert varieties lie at the cross roads of algebraic geometry, combinatorics, commutative algebra, and representation 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.mehr
Verfügbare Formate
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EUR128,39
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Produkt

KlappentextSchubert varieties lie at the cross roads of algebraic geometry, combinatorics, commutative algebra, and representation 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.
Zusammenfassung
Excellent overview of the theory of Schubert varieties

Includes supplementary material: sn.pub/extras
Details
ISBN/GTIN978-3-642-09543-6
ProduktartBuch
EinbandartKartoniert, Paperback
Verlag
Erscheinungsjahr2010
Erscheinungsdatum22.11.2010
AuflageSoftcover reprint of hardcover 1st ed. 2008
ReiheEncyclopaedia of Mathematical Sciences
Seiten266 Seiten
SpracheEnglisch
Gewicht429 g
IllustrationenXIV, 266 p.
Artikel-Nr.10181462

Inhalt/Kritik

Inhaltsverzeichnis
Generalities on algebraic varieties.- Generalities on algebraic groups.- Grassmannian.- Determinantal varieties.- Symplectic Grassmannian.- Orthogonal Grassmannian.- The standard monomial theoretic basis.- Review of GIT.- Invariant theory.- SLn(K)-action.- SOn(K)-action.- Applications of standard monomial theory.mehr
Kritik
From the reviews:



"The goal of the book is to present the results of Classical Invariant Theory (CIT) and Standard Monomial Theory (SMT) and the connection between the two theories. ... The book is written for a broad audience including prospective graduate students and young researchers. The exposition is self-contained. It may be used for a year long course on Invariant Theory and Schubert varieties." (Dmitrii A. Timashëv, Mathematical Reviews, Issue 2008 m)

"The book aims to describe the beautiful connection between Schubert varieties and their Standard Monomial Theory (SMT) on the one hand and Classical Invariant Theory (CIT) on the other. ... make the presentation self-contained keeping in mind the needs of prospective graduate students and young researchers. ... The book may be recommended as a nice introduction to SMT and related active research areas. It may be used for a year long course on Invariant Theory and Schubert varieties." (Ivan V. Arzhantsev, Zentralblatt MATH, Vol. 1137 (15), 2008)mehr