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Construction of the affine Lie algebraA (1)1

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Abstract

We give an explicit construction of the affine Lie algebraA (1)1 as an algebra of differential operators on ℂ[x 1,x 3,x 5, ...]. This algebra is spanned by the creation and annihilation operators and by the homogeneous components of a certain “exponential generating function” which is strikingly similar to the vertex operator in the string model.

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Author notes

  1. James Lepowsky

    Present address: Department of Mathematics, Rutgers University, 08903, New Brunswick, New Jersey, USA

Authors and Affiliations

  1. Department of Mathematics, Yale University, 06520, New Haven, Connecticut, USA

    James Lepowsky

  2. Department of Mathematics, Rutgers University, 08903, New Brunswick, New Jersey, USA

    Robert Lee Wilson

Authors
  1. James Lepowsky
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  2. Robert Lee Wilson
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Additional information

Communicated by A. Jaffe

Partially supported by a Sloan Foundation Fellowship and NSF grant MCS 76-10435

Most of this work was done while the author was a Visiting Fellow at Yale University, supported in part by NSF grant MCS 77-03608 and in part by a Faculty Academic Study Plan grant from Rutgers University

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Lepowsky, J., Wilson, R.L. Construction of the affine Lie algebraA (1)1 . Commun.Math. Phys. 62, 43–53 (1978). https://doi.org/10.1007/BF01940329

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  • DOI: https://doi.org/10.1007/BF01940329

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