Vanishing ideals of lattice diagram determinants

[摘要] A lattice diagram is a finite set L = {(p(1), q(1)),...,(p(n), q(n))} of lattice cells in the positive quadrant. The corresponding lattice diagram determinant is Delta(L)(X-n; Y-n) = det parallel tox(i)(pj) y(i)(qj)parallel to. The space M-L is the space spanned by all partial derivatives of Delta(L)(X-n; Y-n). We denote by M-L(0) the Y-free component of M-L. For mu a partition of n + 1, we denote by mu/ij the diagram obtained by removing the cell (i, j) from the Ferrers diagram of mu. Using homogeneous partially symmetric polynomials, we give here a dual description of the vanishing ideal of the space M-mu(0) and we give the first known description of the vanishing ideal of M-mu/ij(0). (C) 2002 Elsevier Science (USA).

[发布日期] 2002-08-01

[关键词] vanishing ideals;lattice diagram;symmetric modules;harmonic polynomials