Paolo Papi: Covariants in the exterior algebra of a simple Lie algebra

For a simple complex Lie algebra g we study the space of invariants A = (Λg\(\otimes\)g)^g (which describes the isotypic component of type g in Λg) as a module over the algebra of invariants (Λg)^g. As main result we prove that A is a free module, of rank twice the rank of g, over the exterior algebra generated by all primitive invariants in (Λg)^g with the exception of the one of highest degree. We will also discuss generalizations of this result and some related problems. Joint project with C. De Concini and C. Procesi (and partly with P. Moseneder Frajria).