Weyl Character Formula - Weyl Denominator Formula

In the special case of the trivial 1 dimensional representation the character is 1, so the Weyl character formula becomes the Weyl denominator formula:

For special unitary groups, this is equivalent to the expression

\sum_{\sigma \in S_n} \sgn(\sigma) \, X_1^{\sigma(1)-1} \cdots X_n^{\sigma(n)-1} =\prod_{1\le i<j\le n} (X_j-X_i)

for the Vandermonde determinant.

Read more about this topic:  Weyl Character Formula

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