On irreducibility of certain Schur polynomials over fields of finite characteristic

Abstract

We present an elementary proof that the Schur polynomial corresponding to an increasing sequence of exponents (c_0,..., c_{n-1}) with c_0 = 0 is irreducible over every field of characteristic p whenever the numbers d_i = c_{i+1} - c_i are all greater than 1, not divisible by p, and satisfy gcd(d_i, d_{i+1}) = 1 for every i.

arXiv commentThis paper has been withdrawn by the author after he has learned that: - the proof for k=3 had already been independetly invented by Maurizio Monge, in an even more general setting (see arXiv:0903.3192), - the inductive step for k>3 can be as well performed in much closer correspondence to Rajan's original technique, also in a more general setting