Higher-order Sugawara operators for affine Lie algebras

Authors:
Roe Goodman and Nolan R. Wallach

Journal:
Trans. Amer. Math. Soc. **315** (1989), 1-55

MSC:
Primary 17B67; Secondary 15A72, 20G45

DOI:
https://doi.org/10.1090/S0002-9947-1989-0958893-5

MathSciNet review:
958893

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Abstract: Let be the affine Lie algebra associated to a simple Lie algebra . Representations of are described by current fields on the circle and . In this paper a linear map from the symmetric algebra to (formal) operator fields on a suitable category of modules is constructed. The operator fields corresponding to -invariant elements of are called Sugawara fields. It is proved that they satisfy commutation relations of the form

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DOI:
https://doi.org/10.1090/S0002-9947-1989-0958893-5

Article copyright:
© Copyright 1989
American Mathematical Society