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| Main Author: | |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2306.14107 |
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Table of Contents:
- We present a representation of skew-orthogonal polynomials of symplectic type ($β=4$) in terms of a matrix Riemann-Hilbert problem, for weights of the form ${\rm e}^{-V(z)}$ where $V$ is a polynomial of even degree and positive leading coefficient. This is done by representing skew-orthogonality as a kind of multiple-orthogonality. From this, we derive a $β=4$ analogue of the Christoffel-Darboux formula. Finally, our Riemann-Hilbert representation allows us to derive a Lax pair whose compatibility condition may be viewed as a $β=4$ analogue of the Toda lattice.