Standard Monomial Theory

Invariant Theoretic Approach
1. Auflage. Softcover version of original hardcover Auflage 2008
ISBN: 978-3-642-09543-6
Verlag: Springer

Buch, Englisch, Band 137, 266 Seiten, Previously published in hardcover, Format (B × H): 155 mm x 235 mm, Gewicht: 429 g

Reihe: Encyclopaedia of Mathematical Sciences

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.

Zielgruppe

Research

Autoren/Hrsg.

Raghavan, K. N.

Lakshmibai, V.

Fachgebiete

• Mathematik | Informatik Mathematik Mathematik Allgemein Diskrete Mathematik, Kombinatorik
• Mathematik | Informatik Mathematik Algebra Algebraische Strukturen, Gruppentheorie
• Mathematik | Informatik Mathematik Geometrie Algebraische Geometrie

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.