| Résume | Harish-Chandra series of simple modules in finite groups of Lie type in non-defining (positive) characteristic have been introduced more than 20 years ago. By work of Geck, the unipotent modules of the finite unitary groups $GU_n(q)$ are labelled by partitions of $n$. The question of describing the division of the unipotent modules of the unitary groups into Harish-Chandra series is still open. I will present a series of conjectures relating this division with crystal graphs of certain integrable highest weight modules of the quantum group associated to a suitable affine Lie algebra of type A. Of course, I will also give some evidence, experimental as well as theoretical, for these conjectures. This evidence is based upon recent work of Dudas-Malle and Geck-Jacon, as well as on joint work with Thomas Gerber and Nicolas Jacon. |
