Introduction to the Theory of Standard Monomials : Second Edition / by C. S. Seshadri.

Format:

Book

Author/Creator:

Seshadri, C. S., Author.

Series:

Texts and Readings in Mathematics, 2366-8717 ; 46

Language:

English

Subjects (All):

Geometry, Algebraic.

Algebra.

Field theory (Physics).

Algebraic Geometry.

Field Theory and Polynomials.

Local Subjects:

Algebraic Geometry.

Field Theory and Polynomials.

Physical Description:

1 online resource (XVI, 224 p. 20 illus.)

Edition:

1st ed. 2016.

Place of Publication:

Singapore : Springer Singapore : Imprint: Springer, 2016.

Summary:

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.

Contents:

Chapter 1. Schubert Varieties in the Grassmannian

Chapter 2. Standard monomial theory on SLn(k)/Q

Chapter 3. Applications

Chapter 4. Schubert varieties in G/Q.

Notes:

Description based on publisher supplied metadata and other sources.

ISBN:

981-10-1813-8

OCLC:

960708958