BRAID GROUP-RELATED ALGEBRAS, THEIR REPRESENTATIONS AND GENERALIZED HYDROGENLIKE SPECTRA

Representations of the n-braid group where generators are given by mat rices whose elements belong to a noncommutative algebra are discussed. Representation of this algebra in a Hilbert space generalizes the Bur au representation. Two algebras which are closely related and are phys ically indistinguishable provided that a particular eigenvalue is fine tuned are discussed. It is shown that the generalized oscillator syst em given by one of the algebras generates a hydrogenlike spectrum.