Fixed-Lowering ${\mathfrak{sl}}_2$-Triples for Laurent-Shift Operators: Exact Stencil Endpoints and Recurrence Locality

Kyle Singh

Let $S$ be the unit forward shift, and let $$\mathcal{A}=\mathbb{K}[x]⟨S,S^{-1}⟩/(Sx-(x+1)S)$$ be the algebra of finite Laurent-shift operators wit…