Abstract
The nth order index of an irreducible representation of a semisimple compact Lie group, n a nonnegative even integer, is defined as the sum of nth powers of the magnitudes of the weights of the representation. It is shown, in many situations, to have additivity properties similar to those of the dimension under reduction with respect to a subgroup and under reduction of a direct product. The second order index is shown to be Dynkin’s index, multiplied by the rank of the group. Explicit formulas are derived for the fourth order index. A few reduction problems are solved with the help of higher indices as an illustration of their utility.
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