LIBERO WebOPAC Catalogue Display (W561)

Catalogue Information
Field name	Details
Dewey Class	516.35
Title	Standard Monomial Theory ([Ebook]) : Invariant Theoretic Approach / by Venkatramani Lakshmibai, Komaranapuram N. Raghavan.
Author	Lakshmibai, Venkatramani
Added Personal Name	Raghavan, Komaranapuram N.
Other name(s)	SpringerLink (Online service)
Publication	Berlin, Heidelberg : Springer , 2008.
Physical Details	: online resource.
Series	Encyclopaedia of mathematical sciences 0938-0396 ; ; 137
ISBN	9783540767572
Summary Note	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 ubiquitousâthey 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.:
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users).
Internet Site	http://dx.doi.org/10.1007/978-3-540-76757-2
Links to Related Works	Subject References: Algebra . Algebraic Geometry . Geometry, Algebraic . Mathematics . Authors: author . Lakshmibai, Venkatramani . Raghavan, Komaranapuram N. . Corporate Authors: SpringerLink (Online service) . Series: Encyclopaedia of mathematical sciences . Classification: 516.35 . 516.35 (DDC 22) .

Catalogue Display

Standard Monomial Theory: Invariant Theoretic Approach

Reviews