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A Character Formula for Representations of Loop Groups Based by Wendt R.

By Wendt R.

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The parabolic construction. J. Differential Geom. : Some automorphisms of generalized Kac-Moody algebras. J. : The action of Outer Automorphisms on Bundles of Chiral Blocks. Comm. Math. Phys. : From Dynkin diagram symmetries to fixed point structures. Comm. Math. Phys. : The arithmetic theory of loop algebras. J. : The arithmetic theory of loop groups. Publ. Math. : Structure of unitary cocycle representations of loop groups and the group of diffeomorphisms of the circle. J. Reine Angew. Math. : On unstable bundles over elliptic curves.

It turns out that these twisted characters can be identified with untwisted characters of the orbit Lie algebra corresponding to g and σ . 6 Appendix: Some data on affine root systems and their automorphisms The following table lists some data corresponding to the non-simply connected Lie groups. The basic levels of non-simply connected Lie groups have been calculated in [T]. See also [FSS] for a list of the root systems σ for general automorphisms σ of the Dynkin diagram of . The notation for affine root systems in the table below is the same as in [K].

Math. Phys. : From Dynkin diagram symmetries to fixed point structures. Comm. Math. Phys. : The arithmetic theory of loop algebras. J. : The arithmetic theory of loop groups. Publ. Math. : Structure of unitary cocycle representations of loop groups and the group of diffeomorphisms of the circle. J. Reine Angew. Math. : On unstable bundles over elliptic curves. Publ. Res. Inst. Math. Sci. : Infinite-dimensional Lie Algebras. : Lie algebra cohomology and the generalized Borel-Weil theorem. Ann. of Math.

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