Standard Monomial Theory

Invariant Theoretic Approach
2008
ISBN: 978-3-540-76756-5
Verlag: Springer Berlin Heidelberg

Buch, Englisch, Band 137, 266 Seiten, Format (B × H): 160 mm x 241 mm, Gewicht: 588 g

Reihe: Encyclopaedia of Mathematical Sciences

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.

Zielgruppe

Research

Autoren/Hrsg.

Raghavan, K. N.

Lakshmibai, V.

Fachgebiete

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

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.