Symmetric polynomials vanishing on the diagonals shifted by roots of unity
Abstract
For a pair of positive integers (k,r) with r>1 such that k+1 and r-1 are relatively prime, we describe the space of symmetric polynomials in variables x1,...,xn which vanish at all diagonals of codimension k of the form xi=tqsixi-1, i=2,...,k+1, where t and q are primitive roots of unity of orders k+1 and r-1.
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