| Speaker: | Ting Xue (University of Melbourne) |
|---|---|
| Title: | Character sheaves, d-Harish-Chandra series, and affine Springer fibres |
| Date (JST): | Tue, May 13, 2025, 15:30 - 17:00 |
| Place: | Seminar Room A |
| Abstract: | We explain a construction of cuspidal character sheaves via nearby cycles in the setting of cyclically graded Lie algebras. Representations of Hecke algebras of complex reflection groups at roots of unity enter the description of character sheaves. This gives rise to a (conjectural) level-rank duality via connections with Lusztig-Yun’s work, where (Fourier transforms of) character sheaves are related to representations of trigonometric double affine Hecke algebras. We discuss a more general duality arising from d-Harish-Chandra series introduced by Broué-Malle-Michel, as well as connections with Oblomkov-Yun’s construction of rational Cherednik algebra modules using affine Springer fibres. |
