Fock space dualities

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. Key Words: Fock space, classical groups, duality. (author)