Symmetric polynomials vanishing on the diagonals shifted by roots of unity

2002/09/11 by B. Feigin, Feigin, B., M. Jimbo +7
Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #Quantum Algebra (math.QA) #math.CO #math.QA

paper · pdf · doi:10.48550/arxiv.math/0209126

Latex, 13 pages

arxiv created 2002/09/11 · arxiv updated 2009/11/30

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,...,x_n which vanish at all diagonals of codimension k of the form x_i=tq^s_ix_i-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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