Fundamental building blocks of strongly correlated wave functions

The calculation of realistic N-body wave functions for identical fermions is still an open problem in physics, chemistry, and materials science, even for N as small as two. A recently discovered fundamental algebraic structure of many-body Hilbert space allows an arbitrary many-fermion wave function to be written in terms of a finite number of antisymmetric functions called shapes. Shapes naturally generalize the single-Slater-determinant form for the ground state to more than one dimension. Their number is exactly $N{!}^{d-1}$ in $d$ dimensions. An efficient algorithm is described to generate all fermion shapes in spaces of odd dimension, which improves on a recently published general algorithm. The results are placed in the context of contemporary investigations of strongly correlated electrons.