| Abstract: | A survey is given of the method of orbits which makes it possible to construct irreducible unitary representations of an arbitrary Lie group proceeding from mechanical considerations. After a brief introduction to symplectic geometry, a construction of a representation associated with an orbit of a group in the dual space of its Lie algebra is given. Various generalizations of this construction are discussed.Translated from Itogi Nauki i Tekhniki, Seriya Matematicheskii Analiz, Vol. 22, pp. 37–58, 1984. |
