International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 1, Pages 27-63
doi:10.1155/S016117120301233X
Multilocal invariants for the classical groups
Department of Mathematics, Center for Pure and Applied Differential Geometry, KULeuven, Celestijnenlaan 200 B, Leuven 3001, Belgium
Received 11 March 2001
Copyright © 2003 Paul F. Dhooghe. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
Multilocal higher-order invariants, which are higher-order
invariants defined at distinct points of representation space,
for the classical groups are derived in a systematic way. The
basic invariants for the classical groups are the well-known
polynomial or rational invariants as derived from the Capelli
identities. Higher-order invariants are then constructed from the
former ones by means of total derivatives. At each order, it
appears that the invariants obtained in this way do not generate
all invariants. The necessary additional invariants are
constructed from the invariant polynomials on the Lie algebra of
the Lie transformation groups.