On finite-dimensional multiplicity-free irreducible modules for a nil-DAHA of type $(C_1^{\vee },C_1)$

Jongyook Park, Jae-Ho Lee, Hyungtae Baek

Fix nonzero $r_0,r_1\in \mathbb{C}$. Let $\tilde{\mathcal{H}}$ denote a nil-DAHA of type $(C_1^{\vee },C_1)$ defined by generators $t_0,u_0,t_1,u_1$ and relations $(t_i-r_i)(t_i-r_i…