Romanovski polynomials, Gegenbauer connections, and $\mathrm{su}(1,1)$ ladder structures

What the math gives to ML

The paper gives an explicit infinite-dimensional lowest-weight \(\mathrm{su}(1,1)\) representation whose raising and lowering coefficients are known exactly and whose Casimir is fixed by the column index \(\ell\). This is transferable as a structured recurrent or state-space operator: instead of learning a dense transition matrix, use sparse ladder shifts with analytically controlled amplitudes and a diagonal dissipative term. The commutation relations provide an inductive bias for multiscale hidden-state dynamics, while the lowest-weight boundary gives an exact treatment of the first state. The most practical experiment is a truncated \(\mathrm{su}(1,1)\)-structured SSM compared with similarly sized dense, diagonal, and gated recurrent baselines.