9789810241285

Lectures on Infinite Dimensional Lie Algebra

by
  • ISBN13:

    9789810241285

  • ISBN10:

    9810241283

  • Format: Hardcover
  • Copyright: 2001-10-01
  • Publisher: WORLD SCIENTIFIC PUB CO INC
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Supplemental Materials

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Summary

Deals with some of the recent topics involving the representation theory of affine Lie algebras. The book expounds them with examples and detailed calculations.

Table of Contents

Preface vii
Preliminaries on Affine Lie Algebras
1(30)
Affine Lie Algebras
1(17)
Extended Affine Weyl Group
18(7)
Some Formulas for Finite-Dimensional Simple Lie Algebras
25(6)
Characters of Integrable Representations
31(44)
Weyl-Kac Character Formula
31(11)
Specialized Characters
42(7)
Product Expression of Characters
49(9)
Modular Transformation
58(17)
Principal Admissible Weights
75(38)
Admissible Weights
76(7)
Principal Admissible Weights
83(12)
Principal Admissible Weights with IIλ = S(u)
83(6)
Principal Admissible Weights with IIλ = y(S(u))
89(6)
Characters of Principal Admissible Representations
95(5)
Parameterization of Principal Admissible Weights
100(8)
Modular Transformation
108(5)
Residue of Principal Admissible Characters
113(40)
Non-Degenerate Principal Admissible Weights
113(5)
Modular Transformation of Residue
118(10)
Fusion Coefficients
128(25)
The Case gcd(p-p', |J|) = 1
131(3)
The Case gcd(p', |J|) = 1
134(9)
General Case
143(10)
Characters of Affine Orbifolds
153(22)
Characters of Finite Groups
154(8)
Fusion Datum
162(6)
Characters of Affine Orbifolds
168(7)
Operator Calculus
175(64)
Operator Products
175(55)
Boson-Fermion Correspondence
230(9)
Branching Functions
239(48)
Virasoro Modules
239(15)
Virasoro Modules of Central Charge - 22/5
254(9)
Branching Functions
263(9)
Tensor Product Decomposition
272(15)
W-algebra
287(34)
Free Fermionic Fields ψ(z) and ψ*(z)
287(4)
Free Fermionic Fields &phis;(z) and &phis;*(z)
291(3)
Ghost Field Associated to a Simple Lie Algebra
294(3)
BRST Complex
297(4)
Euler-Poincare Characteristics
301(20)
Vertex Representations for Affine Lie Algebras
321(64)
Simple Examples of Vertex Operators
321(15)
The Space C[xi;j ∈N]
322(5)
The Space C[xi;j ∈N odd]
327(9)
Basic Representations of S(2, C)
336(15)
Homogeneous Picture
336(9)
Principal Picture
345(6)
Construction of Basic Representation
351(34)
Homogeneous Picture
352(14)
Principal Picture
366(19)
Soliton Equations
385(44)
Hirota Bilinear Differential Operators
385(2)
KdV Equation and Hirota Bilinear Differential Equations
387(5)
Hirota Equations Associated to the Basic Representation
392(22)
Homogeneous Case
394(10)
Principal Picture
404(10)
Non-Linear Schrodinger Equations
414(15)
Bibliography 429(12)
Index 441

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