Characteristic Classes
In characteristic classes, the Vandermonde polynomial corresponds to the Euler class, and its square (the discriminant) corresponds to the top Pontryagin class. This is formalized in the splitting principle, which connects characteristic classes to polynomials.
From the point of view of stable homotopy theory, the fact that the Euler class is an unstable class corresponds to the fact that alternating polynomials (and the Vandermonde polynomial in particular) are unstable.
Read more about this topic: Alternating Polynomial
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