The fundamental invariants of inhomogeneous classical groups

Abstract

The Casimir operators of the following groups are explicitly constructed :Rn⧠Gl(n,R), Rn⧠Sl(n,R), Rn⧠O(p,q),Cn⧠U(p,q),R2n⧠Sp(n,R), Cn⧠Gl(n,C),Cn⧠Sl(n,C), Cn⧠O(n,C), C2n⧠Sp(n,C), Hn⧠U*(2n), Hn⧠SU*(2n), Hn⧠O*(2n), Hn⧠Sp( p,q), and R⧠(R2n⧠Sp(n,R)). The method is based on a particular fiber bundle structure of the generic orbits generated by the co-adjoint representation of a semidirect product.