Loop groups with infinite dimensional targets and unitary representations
From CRCG-Wiki
The key point in the classical theory of loop groups is the invariant scalar product on the Lie algebra. Therefore it is natural to exploit the extent to which this theory carries over to the situation where the compact target Lie algebra is replaced by a real Hilbert-Lie algebra with an Ad-invariant scalar product. A typical example is the group of unitary operators g for which g -1 is Hilbert Schmidt. In this talk we explain the classification of the 'irreducible' groups showing up in this context and their unitary representations generalizing the highest weight representations of doubly extended loop groups.
