Schur Partial Derivative Operators
Abstract
A lattice diagram is a finite list L=((p_1,q_1),...,(p_n,q_n) of lattice cells. The corresponding lattice diagram determinant is \Delta_L(X;Y)=\det \ x_i^{p_j}y_i^{q_j} \. These lattice diagram determinants are crucial in the study of the socalled ``n! conjecture'' of A. Garsia and M. Haiman. The space M_L is the space spanned by all partial derivatives of \Delta_L(X;Y). The ``shift operators'', which are particular partial symmetric derivative operators are very useful in the comprehension of the structure of the M_L spaces. We describe here how a Schur function partial derivative operator acts on lattice diagrams with distinct cells in the positive quadrant.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 November 2001
 arXiv:
 arXiv:math/0111246
 Bibcode:
 2001math.....11246A
 Keywords:

 Mathematics  Combinatorics;
 05A99;
 05E05;
 05A10
 EPrint:
 8 pages, LaTeX