{"product_id":"standard-monomial-theory-invariant-theoretic-approach-9783642095436","title":"Standard Monomial Theory: Invariant Theoretic Approach","description":"\u003cp\u003e • Author(s): V. Lakshmibai\u003cbr\u003e • Publisher: Springer\u003cbr\u003e • Publisher Imprint: Springer\u003cbr\u003e • BISAC: Geometry - Algebraic\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003e\u003cb\u003eFrom the Back Cover\u003c\/b\u003e\u003cbr\u003e\u003c\/p\u003e\u003cp\u003eSchubert 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.\u003c\/p\u003e \u003cp\u003e\u003c\/p\u003e \u003cp\u003eThis 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.\u003c\/p\u003e \u003cp\u003e\u003c\/p\u003e \u003cp\u003eThe 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.\u003c\/p\u003e","brand":"Springer","offers":[{"title":"Paperback","offer_id":45274898890903,"sku":"9783642095436","price":8732.0,"currency_code":"INR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0666\/3471\/1191\/files\/9783642095436.webp?v=1769281271","url":"https:\/\/atlanticbooks.com\/products\/standard-monomial-theory-invariant-theoretic-approach-9783642095436","provider":"Atlantic Books","version":"1.0","type":"link"}