In their recent work, Lusztig and Yun construct representations of certain graded double affine Hecke algebras (DAHA) using geometry of graded Lie algebras. In joint work (in progress) with Vilonen we study the geometry of graded Lie algebras from another point of view. More precisely, we classify character sheaves in the setting of graded Lie algberas, where representations of Hecke algebras associated with complex reflection groups enter the story. We will explain some conjectures arising from the connection between the above two works, which relate finite dimensional irreducible representations of graded DAHA to irreducible representations of Hecke algebras. If time permits, we will also explain a Schur-Weyl duality conjecture arising from the geometric construction of rational Cherednik algebra modules of Oblomkov and Yun using affine Springer fibres.

The seminar will be hold at RIMS 006