This is a presentation of recent work on quantum permutation groups, complex Hadamard matrices, and the connections between them. A long list of problems is included. We include as well some conjectural statements about matrix models.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc98-0-1, author = {Teodor Banica}, title = {Quantum permutations, Hadamard matrices, and the search for matrix models}, journal = {Banach Center Publications}, volume = {97}, year = {2012}, pages = {11-42}, zbl = {1269.46045}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc98-0-1} }
Teodor Banica. Quantum permutations, Hadamard matrices, and the search for matrix models. Banach Center Publications, Tome 97 (2012) pp. 11-42. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc98-0-1/