Symmetric superspaces and Casimir ghosts.

Casimir ghosts (introduced by physicists Arnaudon, Bauer, Frappat and further studied by the mathematician Gorelik) are very interesting objects which must be used in addition to usual Casimirs in $Z/2Z$-graded (i. e. supersymmetric) situations. We relate Casimir Ghosts to invariant integration and Berezinians on symmetric spaces in supergeometry, and give applications. This is a joint work with Emanuela Petracci.