Abstract
We give an explicit description of the Kac-Peterson-Lepowsky construction of the basic representation for the affine Lie algebraB n (1). Using the conjugacy classes of the Weyl group ofB n, we describe all inequivalent maximal Heisenberg subalgebras of the corresponding affine Lie algebra. We associate to these Heisenberg subalgebras multicomponent charged and neutral free fermionic fields. The boson-fermion correspondence for these fields provides us with fermionic vertex operators, whose ‘normal ordered products’ give the (twisted) vertex operators of the Kac-Peterson-Lepowsky construction.
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This paper was meant as the first paper of a series of two, which would be published inActa Applicandae Mathematicae. Due to some misunderstanding, instead of this manuscript, the paper [32] ‘Level One Representations of the Twisted Affine AlgebrasA (2) n andD (1) n ’ was published in the 1992 issue. This is the reason why the introduction of [32] is rather short, and why there are some misprints in that paper. We take the opportunity to correct some of the errors of [32].
In the title of Section 2.7, in the first line of Section 2.7 (p. 176) and in the title of Section 2.8 (p. 108),gl n(C) should be replaced byso 2n(C). Pages 200 and 201 should be interchanged. The last part of Section 5.5, starting with line 5 on page 212 (‘Notice that:’) and ending with line 17 on page 213 (‘The fourth relation can be proved in an analogous way.’), should be deleted.
The research of J. van de Leur has been made possible by a fellowship of the Royal Netherlands Academy of Arts and Sciences.
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Ten Kroode, F., Van de Leur, J. Level-one representations of the affine lie algebraB (1) n . Acta Appl Math 31, 1–73 (1993). https://doi.org/10.1007/BF01002247
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DOI: https://doi.org/10.1007/BF01002247