Double Affine Hecke Algebras and Congruence Groups - Ion, Bogdan; Sahi, Siddhartha (Memoirs of the American Mathematical Society, 2021)
The most general construction of double affine Artin groups (DAAG) and Hecke algebras (DAHA) associates such objects to pairs of compatible reductive group data. We show that DAAG/DAHA It turns out that the structural intricacies of DAAG/DAHA are captured by the underlying We first give a new Coxeter-type presentation for adjoint DAAG as quotients of the Coxeter braid groups associated to certain crystallographic diagrams that we call double affine Coxeter diagrams. As a consequence we show that the rank two Artin groups of type We show further that the above rank two Artin group action descends to an outer action of the congruence subgroup