A Riemann-Hilbert problem for skew-orthogonal polynomials (Q2480928)

Let \(V\) be a polynomial of degree \(d\). Consider the skew-symmetric form \[ \langle f,g \rangle_1 = \int\int_{\mathbb{R}^2}\,f(x)g(y)\,\text{sign}(x-y)e^{-V(x)-V(y)}\,dx\,dy. \] The author considers a local \((d+1)\times(d+1)\) Riemann-Hilbert problem that characterizes the skew-orthogonal polynomials associated with the form \(\langle\,,\,\rangle_1\).