Weyl made a character formular for SU(m).

Let D1 and D2 be general irreps of SU(m).

kronecker product(D1,D2)= product of characters. There exists a unique decomposition as a sum of characters.

For g in SU(m) there exists h s.t. h^gh=diag(eigenvalues)=diag(e1,...,em) where ei = a pure phase (because of unitarity) and product(ei)=1.

Let Bij=ei^li, Cij=ei^(m-j) where li = number of boxes in the ith row of corresponding young tableau +m (dimension) -i.


if ei=1 => det(B)/det(C)= dim D

jl@crush.caltech.edu index