Double Affine Hecke Algebra in Logarithmic Conformal Field Theory

We construct a representation of the double affine Hecke algebra. The symmetrization of this representation coincides with the center of the quantum group $\overline{\mathscr{U}}_{\mathfrak{q}} s\ell(2)$ and, by Kazhdan–Lusztig duality, with the Verlinde algebra of the $(1,p)$-model of the logarithmic conformal field theory.