Evaluation and spanning sets of confluent Vandermonde forms
arXiv:2209.02523 · doi:10.1063/5.0075576
Abstract
An arbitrary derivative of a Vandermonde form in variables is given as , where the -th variable is differentiated times, . A simple decoding table is introduced to evaluate it by inspection. The special cases where for are in one-to-one correspondence with ribbon Young diagrams. The respective standard ribbon tableaux map to a complete graded basis in the space of -harmonic polynomials. The mapping is realized as an efficient algorithm generating any one of bases with basis elements, both indexed by permutations. The result is placed in the context of a geometric interpretation of the Hilbert space of many-fermion wave functions.
Author's final version accepted in J. Math. Phys., 15 pages, 1 figure