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Abstract

Let Ll=L(sl2l+1,−l−12) be the simple vertex operator algebra based on the affine Lie algebra slˆ2l+1 at boundary admissible level −l−12.We consider a lift ν of the Dynkin diagram involution of A2l=sl2l+1 to an involution of Ll. The ν-twisted Ll-modules are A2l(2)-modules of level −l−12 with an anti-homogeneous realization. We classify simple ν-twisted highest-weight (weak) Ll-modules using twisted Zhu algebras and singular vectors for slˆ2l+1 at level −l−12 obtained by Perše.We find that there are finitely many such modules up to isomorphism, and the ν-twisted (weak) Ll-modules that are in category O for A2l(2) are semi-simple.