HIGHER-ORDER SUGAWARA OPERATORS FOR AFFINE LIE ALGEBRAS

@inproceedings{Wallach2010HIGHERORDERSO,
  title={HIGHER-ORDER SUGAWARA OPERATORS FOR AFFINE LIE ALGEBRAS},
  author={N. Wallach},
  year={2010}
}
Let 0 be the affine Lie algebra associated to a simple Lie algebra 0 . Representations of 0 are described by current fields X(Q on the circle T (X e 0 and £ £ T ). In this paper a linear map a from the symmetric algebra 5(0) to (formal) operator fields on a suitable category of 0 modules is constructed. The operator fields corresponding to 0-invariant elements of S($) are called Sugawara fields. It is proved that they satisfy commutation relations of the form (*) [<t(h)(í), X(t})] = cx,DS{C,ln… CONTINUE READING

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