Statement of Weyl Character Formula
The character of an irreducible representation V of a compact Lie group G is given by
where
- ρ is the half the sum of the positive roots;
- W is the Weyl group;
- λ is the highest weight of the irreducible representation V;
- α runs over the positive roots of the Lie group.
- is the length of the Weyl group element, defined to be the minimal number of reflections with respect to simple roots such that equals the product of those reflections.
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