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Introduction to the Theory of Standard Monomials

2007 Algebra
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Release : 2007
Genre : Algebra
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Book Synopsis Introduction to the Theory of Standard Monomials by : C. S. Seshadri

Download or read book Introduction to the Theory of Standard Monomials written by C. S. Seshadri. This book was released on 2007. Available in PDF, EPUB and Kindle. Book excerpt: "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.

Introduction to the Theory of Standard Monomials

2016-08-22 Mathematics
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Release : 2016-08-22
Genre : Mathematics
Kind : eBook
Book Rating : 138/5 ( reviews)

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Book Synopsis Introduction to the Theory of Standard Monomials by : C. S. Seshadri

Download or read book Introduction to the Theory of Standard Monomials written by C. S. Seshadri. This book was released on 2016-08-22. 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.

Standard Monomial Theory

2007-12-23 Mathematics
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Release : 2007-12-23
Genre : Mathematics
Kind : eBook
Book Rating : 576/5 ( reviews)

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Book Synopsis Standard Monomial Theory by : V. Lakshmibai

Download or read book Standard Monomial Theory written by V. Lakshmibai. This book was released on 2007-12-23. 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.

Contributions to Automorphic Forms, Geometry, and Number Theory

2004-03-11 Mathematics
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Release : 2004-03-11
Genre : Mathematics
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Book Rating : 602/5 ( reviews)

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Book Synopsis Contributions to Automorphic Forms, Geometry, and Number Theory by : Haruzo Hida

Download or read book Contributions to Automorphic Forms, Geometry, and Number Theory written by Haruzo Hida. This book was released on 2004-03-11. Available in PDF, EPUB and Kindle. Book excerpt: In Contributions to Automorphic Forms, Geometry, and Number Theory, Haruzo Hida, Dinakar Ramakrishnan, and Freydoon Shahidi bring together a distinguished group of experts to explore automorphic forms, principally via the associated L-functions, representation theory, and geometry. Because these themes are at the cutting edge of a central area of modern mathematics, and are related to the philosophical base of Wiles' proof of Fermat's last theorem, this book will be of interest to working mathematicians and students alike. Never previously published, the contributions to this volume expose the reader to a host of difficult and thought-provoking problems. Each of the extraordinary and noteworthy mathematicians in this volume makes a unique contribution to a field that is currently seeing explosive growth. New and powerful results are being proved, radically and continually changing the field's make up. Contributions to Automorphic Forms, Geometry, and Number Theory will likely lead to vital interaction among researchers and also help prepare students and other young mathematicians to enter this exciting area of pure mathematics. Contributors: Jeffrey Adams, Jeffrey D. Adler, James Arthur, Don Blasius, Siegfried Boecherer, Daniel Bump, William Casselmann, Laurent Clozel, James Cogdell, Laurence Corwin, Solomon Friedberg, Masaaki Furusawa, Benedict Gross, Thomas Hales, Joseph Harris, Michael Harris, Jeffrey Hoffstein, Hervé Jacquet, Dihua Jiang, Nicholas Katz, Henry Kim, Victor Kreiman, Stephen Kudla, Philip Kutzko, V. Lakshmibai, Robert Langlands, Erez Lapid, Ilya Piatetski-Shapiro, Dipendra Prasad, Stephen Rallis, Dinakar Ramakrishnan, Paul Sally, Freydoon Shahidi, Peter Sarnak, Rainer Schulze-Pillot, Joseph Shalika, David Soudry, Ramin Takloo-Bigash, Yuri Tschinkel, Emmanuel Ullmo, Marie-France Vignéras, Jean-Loup Waldspurger.

A Tribute to C.S. Seshadri

2003-01-01 Mathematics
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Release : 2003-01-01
Genre : Mathematics
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Book Rating : 118/5 ( reviews)

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Book Synopsis A Tribute to C.S. Seshadri by : Lakshmibai V.

Download or read book A Tribute to C.S. Seshadri written by Lakshmibai V.. This book was released on 2003-01-01. Available in PDF, EPUB and Kindle. Book excerpt:

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