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By Wendt R.

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Similarly, the group Wσc = W0 (Twc ) is iso- A character formula for representations of loop groups 579 morphic to the Weyl group of the root system σc . So the character χλ,k closely resembles a character of an irreducible highest weight module of an affine Lie algebra corresponding to the root system σc . 6. Since we are mainly interested in the case of loop groups based on connected but not necessarily simply connected Lie groups G, we restricted our attention to automorphisms σc of the extended Dynkin diagram of which are associated to elements of the center of the universal cover G of G.

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