Abstract: We explain a conjectural generalisation of Uglov’s level-rank (Koszul) duality that arises from d-Harish-Chandra series introduced by Broué-Malle-Michel. BMM were motivated by modular representation theory of finite groups of Lie type. We discuss connections with character sheaves for graded Lie algebras and Oblomkov-Yun’s construction of rational Cherednik algebra modules using affine Springer fibres.

This is based on joint work with Minh-Tam Trinh.