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...
שמור ב:
| Auteurs principaux: | , |
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| מחברים אחרים: | |
| פורמט: | Livre numérique |
| שפה: | Anglais |
| יצא לאור: |
Berlin, Heidelberg :
Springer Berlin Heidelberg
[20..].
Cham : Springer Nature |
| מהדורה: | 1st ed. 2008. |
| סדרה: | Encyclopaedia of Mathematical Sciences
137 |
| נושאים: | |
| גישה מקוונת: | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
| הערה: |
L'impression du document génère 270 p. Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Autres localisations: | Voir dans le Sudoc |
| Edition sous un autre format: | • Standard Monomial Theory, Texte imprimé, 9783642095436 • Standard Monomial Theory, Texte imprimé, 9783540845881 • Standard monomial theory, invariant theoretic approach, Venkatramani Lakshmibai, Komaranapuram N. Raghavan, 2008, Berlin, Springer, 1 vol. (XIV-265 p.), Encyclopaedia of mathematical sciences, 978-3-540-76756-5 |
| סיכום: | 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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| תאור פריט: | L'impression du document génère 270 p. Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| ביבליוגרפיה: | Bibliogr. Index |
| ISBN: | 9783540767572 |
| גישה: | Accès en ligne pour les établissements français bénéficiaires des licences nationales Accès soumis à abonnement pour tout autre établissement Conditions particulières de réutilisation pour les bénéficiaires des licences nationales. https://www.licencesnationales.fr/springer-nature-ebooks-contrat-licence-ln-2017 |