Standard Monomial Theory
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Introduction To The Theory Of Standard Monomials
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Author : C. S. Seshadri
language : en
Publisher:
Release Date : 2014
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 2014 with Geometry, Algebraic categories.
Provides an introduction to what has come to be known as Standard Monomial Theory (SMT). SMT 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 to these groups.
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.
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.
Singular Loci Of Schubert Varieties
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Author : Sara Sarason
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Singular Loci Of Schubert Varieties written by Sara Sarason 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 2012-12-06 with Mathematics categories.
"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.
Introduction To The Theory Of Standard Monomials
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Author : C. S. Seshadri
language : en
Publisher: Hindustan Book Agency and Indian National Science Academy
Release Date : 2007
Introduction To The Theory Of Standard Monomials written by C. S. Seshadri and has been published by Hindustan Book Agency and Indian National Science Academy this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Algebra categories.
"The aim of this book is to give an introduction to what has come to be known as Standard Monomial Theory (SMT). SMT 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 to these groups. The book is a reproduction of a course of Lectures given by the author in 1983-84 which appeared in the Brandeis Lecture Notes series."--BOOK JACKET.
Flag Varieties
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Author : Justin Brown V Lakshmibai
language : en
Publisher:
Release Date : 2018
Flag Varieties written by Justin Brown V Lakshmibai and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018 with categories.
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.
Representation Theories And Algebraic Geometry
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Author : A. Broer
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Representation Theories And Algebraic Geometry written by A. Broer 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 2013-03-09 with Mathematics categories.
The 12 lectures presented in Representation Theories and Algebraic Geometry focus on the very rich and powerful interplay between algebraic geometry and the representation theories of various modern mathematical structures, such as reductive groups, quantum groups, Hecke algebras, restricted Lie algebras, and their companions. This interplay has been extensively exploited during recent years, resulting in great progress in these representation theories. Conversely, a great stimulus has been given to the development of such geometric theories as D-modules, perverse sheafs and equivariant intersection cohomology. The range of topics covered is wide, from equivariant Chow groups, decomposition classes and Schubert varieties, multiplicity free actions, convolution algebras, standard monomial theory, and canonical bases, to annihilators of quantum Verma modules, modular representation theory of Lie algebras and combinatorics of representation categories of Harish-Chandra modules.
Computational Algebraic Geometry
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Author : Frederic Eyssette
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Computational Algebraic Geometry written by Frederic Eyssette 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 2012-12-06 with Mathematics categories.
The theory and practice of computation in algebraic geometry and related domains, from a mathematical point of view, has generated an increasing interest both for its rich theoretical possibilities and its usefulness in applications in science and engineering. In fact, it is one of the master keys for future significant improvement of the computer algebra systems (e.g., Reduce, Macsyma, Maple, Mathematica, Axiom, Macaulay, etc.) that have become such useful tools for many scientists in a variety of disciplines. The major themes covered in this volume, arising from papers p- sented at the conference MEGA-92 were: - Effective methods and complexity issues in commutative algebra, projective geometry, real geometry, and algebraic number theory - Algebra-geometric methods in algebraic computing and applica tions. MEGA-92 was the second of a new series of European conferences on the general theme of Effective Methods in Algebraic Geometry. It was held in Nice, France, on April 21-25, 1992 and built on the themes presented at MEGA-90 (Livomo, Italy, April 17-21, 1990). The next conference - MEGA-94 - will be held in Santander, Spain in the spring of 1994. The Organizing committee that initiatiod and supervises this bi enniel conference consists of A. Conte (Torino), J.H. Davenport (Bath), A. Galligo (Nice), D. Yu. Grigoriev (Petersburg), J. Heintz (Buenos Aires), W. Lassner (Leipzig), D. Lazard (paris), H.M. MOller (Hagen), T. Mora (Genova), M. Pohst (DUsseldort), T. Recio (Santander), J.J.