Infinite Dimensional Lie Algebras
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Infinite Dimensional Lie Algebras: An Introduction(44 Progress in Mathematics)

Infinite Dimensional Lie Algebras: An Introduction(44 Progress in Mathematics)


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About the Book

Table of Contents:
1. Basic definitions.- 2. The invariant bilinear form and the generalized Casimir operator.- 3. Integrable representations and the Weyl group of a Kac-Moody algebra.- 4. Some properties of generalized Cartan matrices.- 5. Real and imaginary roots.- 6. Affine Lie algebras: the normalized invariant bilinear form, the root system and the Weyl group.- 7. Affine Lie algebras: the realization (case k = 1).- 8. Affine Lie algebras: the realization (case k = 2 or 3). Application to the classification of finite order automorphisms.- 9. Highest weight modules over the Lie algebra g(A).- 10. Integrable highest weight modules: the character formula.- 11. Integrable highest weight modules: the weight system, the contravariant Hermitian form and the restriction problem.- 12. Integrable highest weight modules over affine Lie algebras. Application to ?-function identities.- 13. Affine Lie algebras, theta functions and modular forms.- 14. The principal realization of the basic representation. Application to the KdV-type hierarchies of non-linear partial differential equations.- Index of notations and definitions.- References.


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Product Details
  • ISBN-13: 9781475713848
  • Publisher: Birkhauser Boston Inc
  • Publisher Imprint: Birkhauser Boston Inc
  • Height: 229 mm
  • No of Pages: 252
  • Returnable: Y
  • Sub Title: An Introduction
  • ISBN-10: 1475713843
  • Publisher Date: 16 Dec 2012
  • Binding: Paperback
  • Language: English
  • Returnable: Y
  • Series Title: 44 Progress in Mathematics
  • Width: 152 mm


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Infinite Dimensional Lie Algebras: An Introduction(44 Progress in Mathematics)
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Infinite Dimensional Lie Algebras: An Introduction(44 Progress in Mathematics)
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