Assume that $\mathbb{F}$ is an algebraically closed field and let q denote a nonzero scalar in $\mathbb{F}$ that is not a root of unity. The universal DAHA (double affine Hecke algebra) ${\mathfrak{H}}_q$ of type $(C_1^{\vee },C_1)$ is an unital associative $\mathbb{F}$-algebra defined by generators and relations. The generators are $\{t_i^{\pm 1}{\}}_{i=0}^3$ and the relations assert that $\begin{array}{rl}& t_i{t}_i^{-1}=t_i^{-1}{t}_i=1\mathrm{f}\mathrm{o}\mathrm{r}\mathrm{a}\mathrm{l}\mathrm{l}i=0,1,2,3;\\ & t_i+t_i^{-1}\mathrm{i}\mathrm{s}\mathrm{c}\mathrm{e}\mathrm{n}\mathrm{t}\mathrm{r}\mathrm{a}\mathrm{l}\mathrm{f}\mathrm{o}\mathrm{r}\mathrm{a}\mathrm{l}\mathrm{l}i=0,1,2,3;\\ & t_0{t}_1{t}_2{t}_3=q^{-1}.\end{array}$ In this paper we describe the finite-dimensional irreducible ${\mathfrak{H}}_q$-modules from many viewpoints and classify the finite-dimensional irreducible ${\mathfrak{H}}_q$-modules up to isomorphism. The proofs are carried out in the language of linear algebra.

假使，假设$\mathbb{F}$是一个代数闭域，令q表示一个非零标量$\mathbb{F}$这不是团结的根源。通用 DAHA（双仿射 Hecke 代数）${\mathfrak{H}}_q$类型$(C_1^{\vee },C_1)$是单位联想$\mathbb{F}$-由生成器和关系定义的代数。发电机是$\{{吨}_{\mathrm{一世}}^{\pm 1}{\}}_{\mathrm{一世}=0}^3$并且关系断言$\begin{array}{rl}& {吨}_{\mathrm{一世}}{吨}_{\mathrm{一世}}^{-1}={吨}_{\mathrm{一世}}^{-1}{吨}_{\mathrm{一世}}=1\mathrm{F}\mathrm{○}\mathrm{r}\mathrm{一个}\mathrm{l}\mathrm{l}\mathrm{一世}=0,1,2,3;\\ & {吨}_{\mathrm{一世}}+{吨}_{\mathrm{一世}}^{-1}\mathrm{一世}\mathrm{s}\mathrm{C}\mathrm{e}\mathrm{n}\mathrm{吨}\mathrm{r}\mathrm{一个}\mathrm{l}\mathrm{F}\mathrm{○}\mathrm{r}\mathrm{一个}\mathrm{l}\mathrm{l}\mathrm{一世}=0,1,2,3;\\ & {吨}_0{吨}_1{吨}_2{吨}_3=q^{-1}.\end{array}$在本文中，我们描述了有限维不可约${\mathfrak{H}}_q$-从多角度的模块和分类有限维不可约${\mathfrak{H}}_q$-模块直到同构。证明是用线性代数的语言进行的。