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A new method for constructing factorisable representations for current groups and current algebras

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Abstract

LetC ∞ e (R n,G) denote the group of infinitely differentiable maps fromn-dimensional Euclidean space into a simply connected and connected Lie group, which have compact support. This paper introduces a class of factorisable unitary representations ofC ∞ e (R n,G) with the property that the unitary operatorU f corresponding to a functionf inC ∞ e (R n,G) depends not only onf, but also on the derivatives off up to a certain order. In particular these representations can not be extended to the group of all continuous functions fromR n toG with compact support.

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Authors and Affiliations

  1. Mathematics Institute, University of Warwick, CV4 7AL, Coventry, Warwickshire, England

    K. R. Parthasarathy & K. Schmidt

Authors
  1. K. R. Parthasarathy
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  2. K. Schmidt
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Communicated by H. Araki

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Parthasarathy, K.R., Schmidt, K. A new method for constructing factorisable representations for current groups and current algebras. Commun.Math. Phys. 50, 167–175 (1976). https://doi.org/10.1007/BF01617994

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  • DOI: https://doi.org/10.1007/BF01617994

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