We classify the simple integrable modules of double affine Hecke algebras (DAHA) via perverse sheaves. We also get some estimates for the Jordan-Hölder multiplicities of induced modules.
"Induced and simple modules of double affine Hecke algebras." Duke Math. J. 126 (2) 251 - 323, 15 February 2005. https://doi.org/10.1215/S0012-7094-04-12623-5