Standard monomial theory : invariant theoretic approach

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 o...

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Main Authors: Lakshmibai, V., Raghavan, Komaranapuram N.
Format: Book
Language:English
Published: Springer 2017
Subjects:
Online Access:http://repository.vnu.edu.vn/handle/VNU_123/30751
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Institution: Vietnam National University, Hanoi
Language: English
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spelling oai:112.137.131.14:VNU_123-307512020-06-19T01:47:47Z Standard monomial theory : invariant theoretic approach Lakshmibai, V. Raghavan, Komaranapuram N. Mathematics Statistics ; Schubert varieties. 516.353 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 and by many different authors. 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 - the ordinary, orthogonal, and symplectic Grassmannians - on the other. 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. The book also treats, in the last chapter, some other applications of standard monomial theory, e.g., to the study of certain naturally occurring affine algebraic varieties that, like determinantal varieties, can be realized as open parts of Schubert varieties. 2017-04-19T00:36:50Z 2017-04-19T00:36:50Z 2008 Book 978-3-540-76756-5 http://repository.vnu.edu.vn/handle/VNU_123/30751 en 271 p. application/pdf Springer
institution Vietnam National University, Hanoi
building VNU Library & Information Center
country Vietnam
collection VNU Digital Repository
language English
topic Mathematics
Statistics ; Schubert varieties.
516.353
spellingShingle Mathematics
Statistics ; Schubert varieties.
516.353
Lakshmibai, V.
Raghavan, Komaranapuram N.
Standard monomial theory : invariant theoretic approach
description 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 and by many different authors. 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 - the ordinary, orthogonal, and symplectic Grassmannians - on the other. 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. The book also treats, in the last chapter, some other applications of standard monomial theory, e.g., to the study of certain naturally occurring affine algebraic varieties that, like determinantal varieties, can be realized as open parts of Schubert varieties.
format Book
author Lakshmibai, V.
Raghavan, Komaranapuram N.
author_facet Lakshmibai, V.
Raghavan, Komaranapuram N.
author_sort Lakshmibai, V.
title Standard monomial theory : invariant theoretic approach
title_short Standard monomial theory : invariant theoretic approach
title_full Standard monomial theory : invariant theoretic approach
title_fullStr Standard monomial theory : invariant theoretic approach
title_full_unstemmed Standard monomial theory : invariant theoretic approach
title_sort standard monomial theory : invariant theoretic approach
publisher Springer
publishDate 2017
url http://repository.vnu.edu.vn/handle/VNU_123/30751
_version_ 1680968413853253632