Non-standard parametrizations and adjoint invariants of classical groups

We obtain local parametrizations of classical non-compact Lie groups where adjoint invariants under maximal compact subgroups are manifest. Extension to non-compact subgroups is straightforward. As a by-product parametrizatio ns of the same type are obtained for compact groups. They are of physical i nterest in any theory gauge invariant under the adjoint action, typical exa mples being the two dimensional gauged Wess-Zumino-Witten-Novikov models wh ere these coordinatizations become of extreme usefulness to get the backgro und fields representing the vacuum expectation values of the massless modes of the associated (super) string theory. (C) 1999 Elsevier Science B.V. Al l rights reserved.