论文标题
$（C_1^\ vee，C_1）$的通用DAHA的有限维度不可约合模块
Finite-dimensional irreducible modules of the universal DAHA of type $(C_1^\vee,C_1)$
论文作者
论文摘要
假设$ \ mathbb f $是一个代数封闭的字段，让$ q $表示不是unity根部的$ \ mathbb f $中的非零标量。 Universal Daha（Double Affine Hecke代数）$ \ type $的Mathfrak H_Q $（C_1^\ VEE，C_1）$是一个Unital Associative $ \ Mathbb F $ -Algebra，由发电机和关系定义。生成器为$ \ {t_i^{\ pm 1} \} _ {i = 0}^3 $，并且关系断言\ begin {chater*} t_it_i^{ - 1} = t_i^{ - 1} \\ \ hbox {$ t_i+t_i^{ - 1} $ is central} \ quad \ hbox {对于所有$ i = 0,1,1,2,3 $}; \\ T_0T_1T_2T_3 = Q^{ - 1}。 \ end {catch*}在本文中，我们描述了从许多角度来描述有限的不可约合$ \ mathfrak h_q $ - 模块，并对有限的二维不可减少$ \ mathfrak h_q $ -Modules进行分类。这些证明是用线性代数的语言进行的。
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 a 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{gather*} t_it_i^{-1}=t_i^{-1} t_i=1 \quad \hbox{for all $i=0,1,2,3$}; \\ \hbox{$t_i+t_i^{-1}$ is central} \quad \hbox{for all $i=0,1,2,3$}; \\ t_0t_1t_2t_3=q^{-1}. \end{gather*} 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.
