A necessary and sufficient condition is given for reducibility of a symmetric polynomial whose number of variables is large in comparison to degree.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ba53-3-2, author = {A. Schinzel}, title = {Reducibility of Symmetric Polynomials}, journal = {Bulletin of the Polish Academy of Sciences. Mathematics}, volume = {53}, year = {2005}, pages = {251-258}, zbl = {1106.12002}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba53-3-2} }
A. Schinzel. Reducibility of Symmetric Polynomials. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 53 (2005) pp. 251-258. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba53-3-2/