Overview

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.

Full Product Details

Author:   V. Lakshmibai ,  K. N. Raghavan
Publisher:   Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Imprint:   Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Edition:   Softcover reprint of hardcover 1st ed. 2008
Volume:   137
Dimensions:   Width: 15.50cm , Height: 1.40cm , Length: 23.50cm
Weight:   0.454kg
ISBN:  

9783642095436

ISBN 10:   3642095437
Pages:   266
Publication Date:   22 November 2010
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   Out of print, replaced by POD  
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Table of Contents

Reviews

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. Timashev, 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)

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. Timashev, 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)

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. Timashev, 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)

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