= Weyl alternant
{c}
{title2=$A_\nu=\sum_{w\in W}\det(w)e^{w\nu}$}
For a <Weyl group> acting on a <weight lattice>, the displayed element of its <group ring> is alternating: applying $s\in W$ multiplies it by $\det(s)$, by reindexing the sum. It vanishes when $\nu$ is fixed by a root reflection. For the <Weyl vector> $\rho$, it is the <Weyl denominator>. The <Weyl character formula> is the ratio $A_{\lambda+\rho}/A_\rho$. These general root-system alternants specialize to monomial determinants in type A but are not restricted to that type.
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