Generalized fused Specht polynomial basis conjecture for arbitrary Young diagram shapes

Let $\lambda$ be a Young diagram, and let Theorem~ denote the theorem proved in the paper for Young diagrams with two columns, identifying the fused Specht polynomials indexed by $\textnormal{RSYT}^\lambda_\varsigma$ with the corresponding irreducible module structure. General-shape conjecture. Theorem~ holds for Young diagrams of any shape. The paper explains that the linear-independence argument establishing the theorem is currently valid only for Young diagrams with two columns, although the combinatorial formula for fused Specht polynomials holds for arbitrary shapes; extending the theorem is therefore left as a conjectural generalization.