Quantum permutations and complex Hadamard matrices |
| Teodor Banica |
| Abstract |
| A complex Hadamard matrix is a NxN matrix formed by complex numbers of modulus 1, all whose rows are pairwise orthogonal. These matrices seem to play a key role in a number of areas, such as quantum physics, or subfactors. I will survey the basic problematics and the main results, then I will report on some recent work on these matrices, in connection with the quantum permutation groups. |