Abstract
A unitary representation of a, possibly infinite dimensional, Lie group G is called semibounded if the corresponding operators id�(x) from the derived representation are uniformly bounded from above on some non-empty open subset of the Lie algebra g of G. We classify all irreducible semibounded representations of the groups b L'(K) which are double extensions of the twisted loop group L'(K), where K is a simple Hilbert– Lie group (in the sense that the scalar product on its Lie algebra is invariant) and ' is a finite order automorphism of K which leads to one of the 7 irreducible locally affine root systems with their canonicalZ-grading. To achieve this goal, we extend the
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