Abstract
We extend the methods of Pressley and Segal for constructing cocycle representations of the restricted general linear group in infinite-dimensions to the case of a larger linear group modeled by Schatten classes of rank 1≦p<∞. An essential ingredient is the generalization of the determinant line bundle over an infinite-dimensional Grassmannian to the case of an arbitrary Schatten rank,p≧1. The results are used to obtain highest weight representations of current algebras (with the operator Schwinger terms) ind+1-dimensions when the space dimensiond is any odd number.
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Communicated by A. Jaffe
This work is supported in part by funds provided by the U.S. Department of Energy (D.O.E.) under contract #DE-AC02-76ER03069
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Mickelsson, J., Rajeev, S.G. Current algebras ind+1-dimensions and determinant bundles over infinite-dimensional Grassmannians. Commun.Math. Phys. 116, 365–400 (1988). https://doi.org/10.1007/BF01229200
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DOI: https://doi.org/10.1007/BF01229200