= Leading coefficient of an exponential alternant
{title2=$\det(e^{t\ell_i c_j})=t^{\binom m2}\Delta(\ell)\Delta(c)/\prod_{k=0}^{m-1}k!+O(t^{\binom m2+1})$}
For distinct $\ell_i$ and $c_j$, expand the exponential entries in powers of $t$. Nonzero <determinant> terms first occur at the distinct powers $0,1,\ldots,m-1$. The coefficient is the product of their two <Vandermonde determinants> divided by the factorial product. Ratios of such alternants yield the <Weyl dimension formula> by taking a torus <character> to the identity.
Back to article page
