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Construction of standard level one modules for D4n
The Explicit Isomorphism
2-cocycle 2-group 4n _ a,_i a4fc+i a4n _ a4n_2 action acts as _1 affine Lie algebra aia2 aia2ea bilinear form bracket structure Cartan subalgebra central extension choose the maximal compare the eigenvalues Consider the following construct correspondences between characters cosets define the following denote distinct irreducible modules eaep eigenvalues given eigenvector element 7 G Explicit Isomorphism following bracket relations following correspondences following pairs G 2Z given by equations graded dimension h-module Heisenberg algebras Kac-Moody Lie algebra Lemma level one modules linear loduom match vectors maximal abelian subgroup modules are isomorphic modulo nodd normal subgroup Notice obvious that a,a orbifold orthogonal roots pairs of modules Proof quadratic form R/K given remains to show s(cti s(cti s(cti sequence of eigenvalues shorter vector standard level taking inner products term a4n_i Theorem triality vector space weight space write z i=o Z-graded