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Book Cover
Author Seshadri, C. S., author.

Title Introduction to the theory of standard monomials / C.S. Seshadri.

Published New Delhi, India : Hindustan Book Agency, [2014]


Location Call No. Status
Edition Revised, second edition.
Physical description xiv, 221 pages : illustrations ; 24 cm.
Series Texts and readings in mathematics ; 46.
Texts and readings in mathematics ; 46.
Notes Brandeis course lecture notes from the 1983-84 academic year.
Previous edition: 2007.
Bibliography Includes bibliographical references (pages [213]-215) and index.
Contents Schubert varieties in the Grassmannian. Plücker coordinates ; Schubert varieties ; Standard monomials ; Some applications ; Degeneration of Schubert varieties ; Connection with determinantal varieties and invariant theory -- Standard monomial theory on SL[subscript n](k)/Q. Some facts about G/Q ; Young diagrams and standard monomials ; Linear independence of standard monomials ; Some facts about the partial order on W/W[subscript Qi] ; Preparation for the main theorem ; Main theorem ; Another proof for generation by standard monomials -- Applications. Singularities of Schubert varieties ; Vanishing theorem ; Character formula ; Ideal theory of Schubert varieties ; The variety of complexes -- Schubert varieties in G/Q. Some remarks on linear algebraic groups ; Basic properties ; Reduced decompositions ; The normalization map ; Chevalley's multiplicity formula ; Deodhar's Lemma -- Appendix A. Cohen-Macaulay properties / by V. Lakshmibai -- Appendix B. Normality of Schubert varieties -- Appendix C. Standard monomial theory / V. Lakshmibai and C.S. Seshadri.
Original Version Originally published: Waltham, Mass. : Dept. of Mathematics, Brandeis University, 1985. (Brandeis lecture notes ; 4)
Subject Polynomials.
Geometry, Algebraic.
Schubert varieties.
Linear algebraic groups.
ISBN 9789380250588 (paperback)
9380250584 (paperback)