The structure of higher degree symmetry classes of tensors

Abstract

The pape r is concerned with sy mm et ry c lasses of te nso rs whic h a ri se fro m a pe rmut ation gro up C a nd irred uc ible c ha racte r X of C . In case X is o f degree 1, a we ll-kno wn a lgo rith m is ava ilab le fo r induc ing a bas is of the sym me try c lass from the unde rl ying vecto r s pace. Whe n the degree of X is grea te r than 1, no com pa ra ble construc tion has been di scove red . The diffi c ulties are d isc ussed and result s obt a ined in some spec ia l cases.