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Introduction to the theory of standard monomials

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...

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Autor principal: Seshadri, C S
Lenguaje:eng
Publicado: Springer 2016
Materias:
Acceso en línea:https://dx.doi.org/10.1007/978-981-10-1813-8
http://cds.cern.ch/record/2213354
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author Seshadri, C S
author_facet Seshadri, C S
author_sort Seshadri, C S
collection CERN
description 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. d-origin: initial; background-clip: initial; background-position: initial; background-repeat: initial;">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.
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spelling cern-22133542021-04-21T19:31:49Zdoi:10.1007/978-981-10-1813-8http://cds.cern.ch/record/2213354engSeshadri, C SIntroduction to the theory of standard monomialsMathematical Physics and MathematicsThe 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. d-origin: initial; background-clip: initial; background-position: initial; background-repeat: initial;">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.Springeroai:cds.cern.ch:22133542016
spellingShingle Mathematical Physics and Mathematics
Seshadri, C S
Introduction to the theory of standard monomials
title Introduction to the theory of standard monomials
title_full Introduction to the theory of standard monomials
title_fullStr Introduction to the theory of standard monomials
title_full_unstemmed Introduction to the theory of standard monomials
title_short Introduction to the theory of standard monomials
title_sort introduction to the theory of standard monomials
topic Mathematical Physics and Mathematics
url https://dx.doi.org/10.1007/978-981-10-1813-8
http://cds.cern.ch/record/2213354
work_keys_str_mv AT seshadrics introductiontothetheoryofstandardmonomials