Branching functions for winding subalgebras and tensor products (Q753935)

Let \({\mathfrak g}\) be a simple finite-dimensional Lie algebra over \({\mathbb{C}}\), \({\mathfrak g}'={\mathfrak g}\otimes {\mathbb{C}}[t,t^{-1}]\oplus {\mathbb{C}}c\) the nontrivial central extension of the loop algebra, \(\hat{\mathfrak g}={\mathfrak g}\oplus {\mathbb{C}}d/dt.\) A representation \(\pi\) of \({\mathfrak g}'\) in a vector space V is called a positive energy one if \(\pi(c)=kc\), \(k\in {\mathbb{C}}\) and \(\pi\) can be extended to a representation of \(\hat{\mathfrak g}\) so that \(-\pi(d/dt)\) is diagonalizable with non- negative eigenvalues. In this paper the branching coefficients (multiplicities of occurence of an irreducible representation in the tensor product of irreducible representations) are studied for positive energy representations of affine Kac-Moody algebras.