Bombay Lectures On Highest Weight Representations Of Infinite Dimensional Lie Algebras, 2nd Edition

  • Published By: World Scientific Publishing Company
  • ISBN-10: 9814522201
  • ISBN-13: 9789814522205
  • DDC: 512.482
  • Grade Level Range: College Freshman - College Senior
  • 252 Pages | eBook
  • Original Copyright 2013 | Published/Released December 2014
  • This publication's content originally published in print form: 2013

  • Price:  Sign in for price



The first edition of this book is a collection of a series of lectures given by Professor Victor Kac at the TIFR, Mumbai, India in December 1985 and January 1986. These lectures focus on the idea of a highest weight representation, which goes through four different incarnations.The first is the canonical commutation relations of the infinite dimensional Heisenberg Algebra (= oscillator algebra). The second is the highest weight representations of the Lie algebra of infinite matrices, along with their applications to the theory of soliton equations, discovered by Sato and Date, Jimbo, Kashiwara and Miwa. The third is the unitary highest weight representations of the current (= affine Kac-Moody) algebras. These Lie algebras appear in the lectures in connection to the Sugawara construction, which is the main tool in the study of the fourth incarnation of the main idea, the theory of the highest weight representations of the Virasoro algebra.

Table of Contents

Front Cover.
Half Title Page.
Advanced Series in Mathematical Physics.
Title Page.
Copyright Page.
Preface to the Second Edition.
1: Lecture 1.
2: Lecture 2.
3: Lecture 3.
4: Lecture 4.
5: Lecture 5.
6: Lecture 6.
7: Lecture 7.
8: Lecture 8.
9: Lecture 9.
10: Lecture 10.
11: Lecture 11.
12: Lecture 12.
13: Lecture 13.
14: Lecture 14.
15: Lecture 15.
16: Lecture 16.
17: Lecture 17.
18: Lecture 18.