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On an Explicit Isomorphism of Standard Level-One Modules forD̂4n

✍ Scribed by Julie Glass


Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
427 KB
Volume
189
Category
Article
ISSN
0021-8693

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✦ Synopsis


concerned with the construction of vertex operator representations of the affine Kac᎐Moody Lie algebras twisted by automorphisms in H whose restriction to a Cartan subalgebra is q1. These modules are indexed by the four cosets of the root lattice of type D in its dual. The final sections 4 n are devoted to displaying an explicit isomorphism between pairs of modules constructed in the previous sections. Specifically, in Section 10 we show that the two types of modules are graded isomorphic. Sections 11 and 12 contain the final computations in order to display the explicit isomorphisms between the various pairs of modules.

2. THE LIE ALGEBRA

Beginning with an 8 n-dimensional real vector space V ( ‫ޒ‬ 8 n , n g ‫,ގ‬ Ä 4 with orthonormal basis e , e , e , . . . , e , we define the following 0 1 2 8ny1 LEVEL-ONE MODULES OF D 4 n 189 2 Ž .