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Author : Anna B. Veit
Publisher :
ISBN 13 : 9788854878358
Total Pages : 56 pages
Book Rating : 4.8/5 (783 download)
Download or read book Singular Loci of Schubert Varieties and of Rank Varieties. From Scratch written by Anna B. Veit and published by . This book was released on 2014 with total page 56 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Sara Sarason
Publisher : Springer Science & Business Media
ISBN 13 : 146121324X
Total Pages : 254 pages
Book Rating : 4.4/5 (612 download)
Download or read book Singular Loci of Schubert Varieties written by Sara Sarason and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Singular Loci of Schubert Varieties" is a unique work at the crossroads of representation theory, algebraic geometry, and combinatorics. Over the past 20 years, many research articles have been written on the subject in notable journals. In this work, Billey and Lakshmibai have recreated and restructured the various theories and approaches of those articles and present a clearer understanding of this important subdiscipline of Schubert varieties – namely singular loci. The main focus, therefore, is on the computations for the singular loci of Schubert varieties and corresponding tangent spaces. The methods used include standard monomial theory, the nil Hecke ring, and Kazhdan-Lusztig theory. New results are presented with sufficient examples to emphasize key points. A comprehensive bibliography, index, and tables – the latter not to be found elsewhere in the mathematics literature – round out this concise work. After a good introduction giving background material, the topics are presented in a systematic fashion to engage a wide readership of researchers and graduate students.
Author : V Lakshmibai
Publisher : Springer
ISBN 13 : 9811313938
Total Pages : 312 pages
Book Rating : 4.8/5 (113 download)
Download or read book Flag Varieties written by V Lakshmibai and published by Springer. This book was released on 2018-06-26 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book discusses the importance of flag varieties in geometric objects and elucidates its richness as interplay of geometry, combinatorics and representation theory. The book presents a discussion on the representation theory of complex semisimple Lie algebras, as well as the representation theory of semisimple algebraic groups. In addition, the book also discusses the representation theory of symmetric groups. In the area of algebraic geometry, the book gives a detailed account of the Grassmannian varieties, flag varieties, and their Schubert subvarieties. Many of the geometric results admit elegant combinatorial description because of the root system connections, a typical example being the description of the singular locus of a Schubert variety. This discussion is carried out as a consequence of standard monomial theory. Consequently, this book includes standard monomial theory and some important applications—singular loci of Schubert varieties, toric degenerations of Schubert varieties, and the relationship between Schubert varieties and classical invariant theory. The two recent results on Schubert varieties in the Grassmannian have also been included in this book. The first result gives a free resolution of certain Schubert singularities. The second result is about certain Levi subgroup actions on Schubert varieties in the Grassmannian and derives some interesting geometric and representation-theoretic consequences.
Author : William Fulton
Publisher : Springer
ISBN 13 : 3540698043
Total Pages : 158 pages
Book Rating : 4.5/5 (46 download)
Download or read book Schubert Varieties and Degeneracy Loci written by William Fulton and published by Springer. This book was released on 2006-11-13 with total page 158 pages. Available in PDF, EPUB and Kindle. Book excerpt: Schubert varieties and degeneracy loci have a long history in mathematics, starting from questions about loci of matrices with given ranks. These notes, from a summer school in Thurnau, aim to give an introduction to these topics, and to describe recent progress on these problems. There are interesting interactions with the algebra of symmetric functions and combinatorics, as well as the geometry of flag manifolds and intersection theory and algebraic geometry.
Author : Jaime Gutierrez
Publisher : Springer
ISBN 13 : 3319150812
Total Pages : 222 pages
Book Rating : 4.3/5 (191 download)
Download or read book Computer Algebra and Polynomials written by Jaime Gutierrez and published by Springer. This book was released on 2015-01-20 with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algebra and number theory have always been counted among the most beautiful mathematical areas with deep proofs and elegant results. However, for a long time they were not considered that important in view of the lack of real-life applications. This has dramatically changed: nowadays we find applications of algebra and number theory frequently in our daily life. This book focuses on the theory and algorithms for polynomials over various coefficient domains such as a finite field or ring. The operations on polynomials in the focus are factorization, composition and decomposition, basis computation for modules, etc. Algorithms for such operations on polynomials have always been a central interest in computer algebra, as it combines formal (the variables) and algebraic or numeric (the coefficients) aspects. The papers presented were selected from the Workshop on Computer Algebra and Polynomials, which was held in Linz at the Johann Radon Institute for Computational and Applied Mathematics (RICAM) during November 25-29, 2013, at the occasion of the Special Semester on Applications of Algebra and Number Theory.
Author : Venkatrama Lakshmibai
Publisher : Springer Science & Business Media
ISBN 13 : 9783764304447
Total Pages : 598 pages
Book Rating : 4.3/5 (44 download)
Download or read book A Tribute to C.S. Seshadri written by Venkatrama Lakshmibai and published by Springer Science & Business Media. This book was released on 2003-07-24 with total page 598 pages. Available in PDF, EPUB and Kindle. Book excerpt: C.S. Seshadri turned seventy on the 29th of February, 2002. To mark this occasion, a symposium was held in Chennai, India, where some of his colleagues gave expository talks highlighting Seshadri's contributions to mathematics. This volume includes expanded texts of these talks as well as research and expository papers on geometry and representation theory. It will serve as an excellent reference for researchers and students in these areas.
Author : Christian Kassel
Publisher :
ISBN 13 :
Total Pages : 37 pages
Book Rating : 4.:/5 (538 download)
Download or read book The Singular Locus of a Schubert Variety written by Christian Kassel and published by . This book was released on 2001 with total page 37 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Laurent Manivel
Publisher : American Mathematical Soc.
ISBN 13 : 9780821821541
Total Pages : 180 pages
Book Rating : 4.8/5 (215 download)
Download or read book Symmetric Functions, Schubert Polynomials and Degeneracy Loci written by Laurent Manivel and published by American Mathematical Soc.. This book was released on 2001 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text grew out of an advanced course taught by the author at the Fourier Institute (Grenoble, France). It serves as an introduction to the combinatorics of symmetric functions, more precisely to Schur and Schubert polynomials. Also studied is the geometry of Grassmannians, flag varieties, and especially, their Schubert varieties. This book examines profound connections that unite these two subjects. The book is divided into three chapters. The first is devoted to symmetricfunctions and especially to Schur polynomials. These are polynomials with positive integer coefficients in which each of the monomials correspond to a Young tableau with the property of being ``semistandard''. The second chapter is devoted to Schubert polynomials, which were discovered by A. Lascoux andM.-P. Schutzenberger who deeply probed their combinatorial properties. It is shown, for example, that these polynomials support the subtle connections between problems of enumeration of reduced decompositions of permutations and the Littlewood-Richardson rule, a particularly efficacious version of which may be derived from these connections. The final chapter is geometric. It is devoted to Schubert varieties, subvarieties of Grassmannians, and flag varieties defined by certain incidenceconditions with fixed subspaces. This volume makes accessible a number of results, creating a solid stepping stone for scaling more ambitious heights in the area. The author's intent was to remain elementary: The first two chapters require no prior knowledge, the third chapter uses some rudimentary notionsof topology and algebraic geometry. For this reason, a comprehensive appendix on the topology of algebraic varieties is provided. This book is the English translation of a text previously published in French.
Author : Lakshmibai V.
Publisher : Springer
ISBN 13 : 9386279118
Total Pages : 574 pages
Book Rating : 4.3/5 (862 download)
Download or read book A Tribute to C.S. Seshadri written by Lakshmibai V. and published by Springer. This book was released on 2003-01-01 with total page 574 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : V. Lakshmibai
Publisher : Springer Science & Business Media
ISBN 13 : 3540767576
Total Pages : 271 pages
Book Rating : 4.5/5 (47 download)
Download or read book Standard Monomial Theory written by V. Lakshmibai and published by Springer Science & Business Media. This book was released on 2007-12-23 with total page 271 pages. Available in PDF, EPUB and Kindle. Book excerpt: Schubert varieties provide an inductive tool for studying flag varieties. 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 on the other.
Author : Stanisław Balcerzyk
Publisher :
ISBN 13 : 9788301095796
Total Pages : 520 pages
Book Rating : 4.0/5 (957 download)
Download or read book Topics in Algebra written by Stanisław Balcerzyk and published by . This book was released on 1990 with total page 520 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Jennifer Koonz
Publisher :
ISBN 13 :
Total Pages : 92 pages
Book Rating : 4.:/5 (881 download)
Download or read book Properties of Singular Schubert Varieties written by Jennifer Koonz and published by . This book was released on 2013 with total page 92 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author :
Publisher :
ISBN 13 :
Total Pages : 900 pages
Book Rating : 4.3/5 (91 download)
Download or read book Mathematical Reviews written by and published by . This book was released on 2006 with total page 900 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : C. S. Seshadri
Publisher : Springer
ISBN 13 : 9811018138
Total Pages : 229 pages
Book Rating : 4.8/5 (11 download)
Download or read book Introduction to the Theory of Standard Monomials written by C. S. Seshadri and published by Springer. This book was released on 2016-08-22 with total page 229 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is a reproduction of a course of lectures delivered by the author in 1983-84 which appeared in the Brandeis Lecture Notes series. The aim of this course was to give an introduction to the series of papers by concentrating on the case of the full linear group. In recent years, there has been great progress in standard monomial theory due to the work of Peter Littelmann. The author’s lectures (reproduced in this book) remain an excellent introduction to standard monomial theory. Standard monomial theory deals with the construction of nice bases of finite dimensional irreducible representations of semi-simple algebraic groups or, in geometric terms, nice bases of coordinate rings of flag varieties (and their Schubert subvarieties) associated with these groups. Besides its intrinsic interest, standard monomial theory has applications to the study of the geometry of Schubert varieties. Standard monomial theory has its origin in the work of Hodge, giving bases of the coordinate rings of the Grassmannian and its Schubert subvarieties by “standard monomials”. In its modern form, standard monomial theory was developed by the author in a series of papers written in collaboration with V. Lakshmibai and C. Musili. In the second edition of the book, conjectures of a standard monomial theory for a general semi-simple (simply-connected) algebraic group, due to Lakshmibai, have been added as an appendix, and the bibliography has been revised.
Author : American Mathematical Society
Publisher :
ISBN 13 :
Total Pages : 678 pages
Book Rating : 4.E/5 ( download)
Download or read book Abstracts of Papers Presented to the American Mathematical Society written by American Mathematical Society and published by . This book was released on 2000 with total page 678 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Venkatramani Lakshmibai
Publisher : Editions Hermann
ISBN 13 :
Total Pages : 342 pages
Book Rating : 4.E/5 ( download)
Download or read book Flag Varieties written by Venkatramani Lakshmibai and published by Editions Hermann. This book was released on 2001 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt: Flag varieties constitute an important class of homogeneous spaces. Because of their rich geometry and combinatorics, they represent fundamental objects in the areas of Algebraic Geometry, Algebraic Groups and Representation Theory. This book provides an introduction to the subject, and presents the interplay of flag varieties among Geometry, Combinatorics and Representation Theory. The Schubert subvarieties provide a powerful inductive machinery for the study of flag varieties. The central theme of this book is the theory of Schubert varieties - their geometric properties, ideal theory, singularity theory. This book also presents the relationship between Schubert varieties and certain affine varieties - classical determinantal varieties, ladder determinantal varieties, quiver varieties. varieties of complexes, certain affine toric varieties. This book includes a detailed treatment of the classical determinantal varieties, their normality, Cohen-Macaulayness, singular loci, relationship to classical invariant theory : the treatment uses their relationship to Schubert varieties.
Author : Jean-Luc Brylinski
Publisher : Springer Science & Business Media
ISBN 13 : 1461202612
Total Pages : 629 pages
Book Rating : 4.4/5 (612 download)
Download or read book Lie Theory and Geometry written by Jean-Luc Brylinski and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 629 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume, dedicated to Bertram Kostant on the occasion of his 65th birthday, is a collection of 22 invited papers by leading mathematicians working in Lie theory, geometry, algebra, and mathematical physics. Kostant’s fundamental work in all these areas has provided deep new insights and connections, and has created new fields of research. The papers gathered here present original research articles as well as expository papers, broadly reflecting the range of Kostant’s work.
