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OverviewSchubert 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. Full Product DetailsAuthor: Venkatramani Lakshmibai , Komaranapuram N RaghavanPublisher: Springer Imprint: Springer ISBN: 9786611148225ISBN 10: 6611148221 Pages: 271 Publication Date: 01 January 2008 Audience: General/trade , General Format: Electronic book text Publisher's Status: Active Availability: Out of stock ![]() The supplier is temporarily out of stock of this item. It will be ordered for you on backorder and shipped when it becomes available. Table of ContentsReviewsAuthor InformationTab Content 6Author Website:Countries AvailableAll regions |