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- https://academic.oup.com/imajna/advance-article/doi/10.1093/imanum/draa011/5838512?guestAccessKey=2f1a853e-8c25-46e3-8e69-900d4126c56e
Final published version

Discrete orthogonality relations for Hall-Littlewood polynomials are employed, so as to derive cubature rules for the integration of homogeneous symmetric functions with respect to the density of the circular unitary ensemble (which originates from the Haar measure on the special unitary group $SU(n;\mathbb{C})$). By passing to Macdonald's hyperoctahedral Hall-Littlewood polynomials, we moreover find analogous cubature rules for the integration with respect to the density of the circular quaternion ensemble (which originates in turn from the Haar measure on the compact symplectic group $Sp (n;\mathbb{H})$). The cubature formulas under consideration are exact for a class of rational symmetric functions with simple poles supported on a prescribed complex hyperplane arrangement. In the planar situations (corresponding to $SU(3;\mathbb{C})$ and $Sp (2;\mathbb{H})$), a determinantal expression for the Christoffel weights enables us to write down compact cubature rules for the integration over the equilateral triangle and the isosceles right triangle, respectively.

Original language | English |
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Number of pages | 33 |

Journal | IMA Journal of Numerical Analysis |

DOIs | |

Publication status | E-pub ahead of print - 21 May 2020 |

- Cubature rules, Hall–Littlewood polynomials, random matrices, compact classical Lie groups, Haar measures

ID: 73144407