I am looking for a proof of the statement:
Every antisymmetric (alternating) polynomial is divisible by Vandermonde product, yielding a symmetric polynomial in the result.
The statement is really helpful in constructing further Schur polynomials theory.
I came across it reading David M. Bressoud "Exploiting Symmetries: Alternating-Sign Matrices and the Weyl Character Formulas" and can be seen here in the context http://link.springer.com/chapter/10.1007%2F978-0-387-78510-3_3#page-1
According to the author, the orginal statement has been proven by Cauchy in "Mémoire sur les fonctions qui ne peuvent obtenir que deux valeurs égales et de signes contraires par suite des transpositions opérées entre les variables qu'elles renferment", which can be viewed here: http://math-doc.ujf-grenoble.fr/cgi-bin/oeitem?id=OE_CAUCHY_2_1_91_0
Unfortunately it is only available in French, which makes it impossible for me to digest.
I really appreciate your help!