  Several cases of Fock space duality occurring in the theory of many-body
systems in general and nuclei in particular are discussed. All of them are
special cases of a general duality theorem proved in mathematics by Howe in the
1970s. Dualities on a fermion Fock space between orthogonal Lie algebras and
related groups, including an o-Pin duality recently discovered by the author,
present a nice, symmetric pattern.
