Generalized Double Affine Hecke Algebra for Double Torus

We propose a generalization of the double affine Hecke algebra of type-C C1 at specific parameters by introducing a ``Heegaard dual’’ of the Hecke operators. Shown is a relationship with the skein algebra on double torus. We give automorphisms of the algebra associated with the Dehn twists on the double torus.