An Infinite-Dimensional ${\square }_q$-Module Obtained from the $q$-Shuffle Algebra for Affine ${\mathfrak{sl}}_2$

Sarah Post, Paul Terwilliger

Let $\mathbb{F}$ denote a field, and pick a nonzero $q\in \mathbb{F}$ that is not a root of unity. Let ${\mathbb{Z}}_4=\mathbb{Z}/4\mathbb{Z}$ denote the cyclic group of order 4. Define…