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Standard Monomial Theory: Invariant Theoretic Approach: 137 (Encyclopaedia of Mathematical Sciences, 137) - Tapa dura

Libro 42 de 47: Encyclopaedia of Mathematical Sciences

Raghavan, K. N.; Lakshmibai, V.

 
9783540767565: Standard Monomial Theory: Invariant Theoretic Approach: 137 (Encyclopaedia of Mathematical Sciences, 137)
Tapa dura
ISBN 10: 3540767568 ISBN 13: 9783540767565
Editorial: Springer, 2008

Sinopsis

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.

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De la contraportada

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.

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Editorial
Springer
Año de publicación
2008
Idioma
Inglés
ISBN 10 
3540767568
ISBN 13 
9783540767565
Encuadernación
Tapa dura
Número de páginas
280
Contacto del fabricante
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Poststr. 9
Darmstadt
64293
Alemania

Otras ediciones populares con el mismo título

9783642095436: Standard Monomial Theory: Invariant Theoretic Approach: 137 (Encyclopaedia of Mathematical Sciences)

Edición Destacada

ISBN 10:  3642095437 ISBN 13:  9783642095436
Editorial: Springer, 2010
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