Affine Lie algebras of

Twisted vertex operator representation of

Let be the -twisted affine Lie algebra of , and be the corresponding -natural Heisenberg module on . Defining

we construct the twisted vertex operator

where the second expression used the Normal ordered product. Skipping over a lot of detail1, the representation of on extends to precisely two irreducible representations

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Footnotes

  1. 1988. Vertex operator algebras and the Monster, §3, pp. 61ff. ↩