Finite-dimensional irreducible modules of the universal DAHA of type (C ₁^∨,C ₁)

Assume that (Formula presented.) is an algebraically closed field and let q denote a nonzero scalar in (Formula presented.) that is not a root of unity. The universal DAHA (double affine Hecke algebra) (Formula presented.) of type (Formula presented.) is an unital associative (Formula presented.) -algebra defined by generators and relations. The generators are (Formula presented.) and the relations assert that (Formula presented.) In this paper we describe the finite-dimensional irreducible (Formula presented.) -modules from many viewpoints and classify the finite-dimensional irreducible (Formula presented.) -modules up to isomorphism. The proofs are carried out in the language of linear algebra.