| Description |
For finite dimensional simple and ffine Lie algebras, the roots of positive norm are all real, i.e. act locally finitely on integrable modules, whereas the roots of non-positive norm do not, and the nondiagonal entries of the Cartan matrices are non-positive. For most finite dimensional and affine Lie superalgebras there are roots both positive and negative non-diagonal entries in the Cartan matrices. Hence the usual proofs aof the character formula do not work and computing these characters in all cases has remained an open problem for the last twenty years. The greater the dimension of the maximal isotropic, subspace of the set of roots, the greater the complication. In this talk, I will explain my recent proof of these formulae.
|