Highest weight representations of quantum current algebras (Q1912355)

The authors suggest a construction of highest weight representations for a quantum current algebra \(\text{Map} (X,A_q)\) where \(X\) is a manifold and \(A_q\) is a \(q\)-deformation of the universal enveloping algebra of a Lie algebra \(A\). The construction relies on taking the direct integral over \(X\) of representation spaces for the algebra \(A_q\) and then passing to the Fock space. A particular case is considered when \(X=D\) -- the unit disk in the complex plane and \(A=\text{sl} (2,\mathbb{C})\).