Generalized double affine Hecke algebra for double torus (Q6606282)

In the paper under review a generalization of the double affine Hecke algebra of type \(C^{\vee}C^1\) at specific parameters is proposed by introducing a ``Heegaard dual'' of the Hecke operators. This generalization is based on a paper [\textit{K. Hikami}, Lett. Math. Phys. 109, No. 10, 2305--2358 (2019; Zbl 1458.57011)], where representation of the skein algebra on the surface \(\Sigma_{2,0}\) was given.\N\NThe constructed generalization differs from a generalization in [\textit{P. Etingof} et al., Adv. Math. 212, No. 2, 749--796 (2007; Zbl 1118.14003)].