TY - JOUR AU - Chien, Tuan-Yow AU - Waldron, Shayne PY - 2018/12/31 Y2 - 2024/03/29 TI - The Projective Symmetry Group of a Finite Frame JF - New Zealand Journal of Mathematics JA - NZ J Math VL - 48 IS - 0 SE - Articles DO - 10.53733/35 UR - https://www.nzjmath.org/index.php/NZJMATH/article/view/35 SP - 55-81 AB - <p>We define the <em>projective symmetry group</em> of a finite sequence of vectors (a frame) in a natural way as a group of permutations on the vectors (or their indices). This definition ensures that the projective symmetry group is the same for a frame and its complement. We give an algorithm for computing the projective symmetry group from a small set of projective invariants when the underlying field is a subfield of <img class="tex" src="http://nzjm.math.auckland.ac.nz/images/math/f/0/b/f0b01fe0a1eec87c634584ac0694fb71.png" alt="\mathbb{C}"> which is closed under conjugation. This algorithm is applied in a number of examples including equiangular lines (in particular SICs), MUBs, and harmonic frames.</p> ER -