ABSTRACT

There are a couple of different useful bases for the SU(N) generators. This chapter starts with a generalization of the Gell-Mann matrices, in which we build up from the SU(N) to SU(N + 1) generators one step at a time. Because of the antisymmetry, no two indices can take on the same value. The highest weight of any irreducible representation can be written in terms of the Dynkin coefficients. Clebsch-Gordan decomposition works the same way as for SU(3), except that now we need cs for the third row of the tableau, ds for the fourth, etc. A hook is a line passing vertically up through the bottom of some column of boxes, making a right hand turn in some box and passing out through the row of boxes.