Introduction To The Theory Of Standard Monomials
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Introduction To The Theory Of Standard Monomials
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Author : C. S. Seshadri
language : en
Publisher:
Release Date : 1985
Introduction To The Theory Of Standard Monomials written by C. S. Seshadri and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985 with Algebra categories.
Introduction To The Theory Of Standard Monomials
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Author : C. S. Seshadri
language : en
Publisher: Springer
Release Date : 2016-08-22
Introduction To The Theory Of Standard Monomials written by C. S. Seshadri and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-08-22 with Mathematics categories.
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.
Standard Monomial Theory
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Author : V. Lakshmibai
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-12-23
Standard Monomial Theory written by V. Lakshmibai and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-12-23 with Mathematics categories.
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.
Atiyah Singer Index Theorem An Introduction
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Author : Amiya Mukherjee
language : en
Publisher: Springer
Release Date : 2013-10-30
Atiyah Singer Index Theorem An Introduction written by Amiya Mukherjee and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-10-30 with Mathematics categories.
This monograph is a thorough introduction to the Atiyah-Singer index theorem for elliptic operators on compact manifolds without boundary. The main theme is only the classical index theorem and some of its applications, but not the subsequent developments and simplifications of the theory. The book is designed for a complete proof of the K -theoretic index theorem and its representation in terms of cohomological characteristic classes. In an effort to make the demands on the reader's knowledge of background materials as modest as possible, the author supplies the proofs of almost every result. The applications include Hirzebruch signature theorem, Riemann-Roch-Hirzebruch theorem, and the Atiyah-Segal-Singer fixed point theorem, etc.
A Tribute To C S Seshadri
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Author : Venkatrama Lakshmibai
language : en
Publisher: Springer Science & Business Media
Release Date : 2003-07-24
A Tribute To C S Seshadri written by Venkatrama Lakshmibai and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-07-24 with Mathematics categories.
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.
Theory Of Semigroups And Applications
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Author : Kalyan B. Sinha
language : en
Publisher: Springer
Release Date : 2017-07-12
Theory Of Semigroups And Applications written by Kalyan B. Sinha and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-07-12 with Mathematics categories.
The book presents major topics in semigroups, such as operator theory, partial differential equations, harmonic analysis, probability and statistics and classical and quantum mechanics, and applications. Along with a systematic development of the subject, the book emphasises on the explorations of the contact areas and interfaces, supported by the presentations of explicit computations, wherever feasible. Designed into seven chapters and three appendixes, the book targets to the graduate and senior undergraduate students of mathematics, as well as researchers in the respective areas. The book envisages the pre-requisites of a good understanding of real analysis with elements of the theory of measures and integration, and a first course in functional analysis and in the theory of operators. Chapters 4 through 6 contain advanced topics, which have many interesting applications such as the Feynman–Kac formula, the central limit theorem and the construction of Markov semigroups. Many examples have been given in each chapter, partly to initiate and motivate the theory developed and partly to underscore the applications. The choice of topics in this vastly developed book is a difficult one, and the authors have made an effort to stay closer to applications instead of bringing in too many abstract concepts.
Representation Theory Number Theory And Invariant Theory
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Author : Jim Cogdell
language : en
Publisher: Birkhäuser
Release Date : 2017-10-19
Representation Theory Number Theory And Invariant Theory written by Jim Cogdell and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-10-19 with Mathematics categories.
This book contains selected papers based on talks given at the "Representation Theory, Number Theory, and Invariant Theory" conference held at Yale University from June 1 to June 5, 2015. The meeting and this resulting volume are in honor of Professor Roger Howe, on the occasion of his 70th birthday, whose work and insights have been deeply influential in the development of these fields. The speakers who contributed to this work include Roger Howe's doctoral students, Roger Howe himself, and other world renowned mathematicians. Topics covered include automorphic forms, invariant theory, representation theory of reductive groups over local fields, and related subjects.
Young Tableaux In Combinatorics Invariant Theory And Algebra
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Author : Joseph P.S. Kung
language : en
Publisher: Elsevier
Release Date : 2014-05-12
Young Tableaux In Combinatorics Invariant Theory And Algebra written by Joseph P.S. Kung and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-12 with Mathematics categories.
Young Tableaux in Combinatorics, Invariant Theory, and Algebra: An Anthology of Recent Work is an anthology of papers on Young tableaux and their applications in combinatorics, invariant theory, and algebra. Topics covered include reverse plane partitions and tableau hook numbers; some partitions associated with a partially ordered set; frames and Baxter sequences; and Young diagrams and ideals of Pfaffians. Comprised of 16 chapters, this book begins by describing a probabilistic proof of a formula for the number f? of standard Young tableaux of a given shape f?. The reader is then introduced to the generating function of R. P. Stanley for reverse plane partitions on a tableau shape; an analog of Schensted's algorithm relating permutations and triples consisting of two shifted Young tableaux and a set; and a variational problem for random Young tableaux. Subsequent chapters deal with certain aspects of Schensted's construction and the derivation of the Littlewood-Richardson rule for the multiplication of Schur functions using purely combinatorial methods; monotonicity and unimodality of the pattern inventory; and skew-symmetric invariant theory. This volume will be helpful to students and practitioners of algebra.
Flag Varieties
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Author : V Lakshmibai
language : en
Publisher: Springer
Release Date : 2018-06-26
Flag Varieties written by V Lakshmibai and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-06-26 with Mathematics categories.
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.
Arithmetic And Geometry
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Author : Michael Artin
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-11
Arithmetic And Geometry written by Michael Artin and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-11 with Mathematics categories.