Carl Stigner: Mapping class group representations from affine Lie algebras - reducibility and CFT-boundary conditions
From CRCG-Wiki
The category of representations of an affine Lie algebra at fixed level can be endowed with a tensor product which arises in a natural way from conformal blocks. The complexification of the corresponding Grothendieck ring is the Verlinde algebra. We establish that conformal blocks also give rise to another semisimple commutative associative algebra A, whose irreducible representations are in bijection with the elementary boundary conditions of the CFT. The structure constants of A can be expressed as the invariant of a ribbon graph in a three-manifold. This graph defines an intertwiner of the representation of the mapping class group on the conformal blocks and thus gives information about the reducibility of that representation.
Joint work with J. Fuchs & C. Schweigert.
