Infinite Dimensional Lie Algebras

An Introduction

AvVictor G. Kac

Häftad, Engelska, 2012

Del 44 i serien Progress in Mathematics

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Produktinformation

Utgivningsdatum:2012-12-16
Mått:152 x 229 x 15 mm
Vikt:399 g
Format:Häftad
Språk:Engelska
Serie:Progress in Mathematics
Antal sidor:252
Upplaga:1983
Förlag:Birkhauser Boston Inc
ISBN:9781475713848

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Innehållsförteckning

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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