Gaussian cubature arising from hybrid characters of simple Lie groups

Abstract

Lie groups with two different root lengths allow two mixed sign homomorphisms on their corresponding Weyl groups, which in turn give rise to two families of hybrid Weyl group orbit functions and characters. In this paper we extend the ideas leading to the Gaussian cubature formulas for families of polynomials arising from the characters of irreducible representations of any simple Lie group, to new cubature formulas based on the corresponding hybrid characters. These formulas are new forms of Gaussian cubature in the short root length case and new forms of Radau cubature in the long root case. The nodes for the cubature arise quite naturally from the (computationally efficient) elements of finite order of the Lie group.

arXiv comment23 pages, 3 figures

References in corpus (8)

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• E-Orbit Functions
• (Anti)symmetric multivariate trigonometric functions and corresponding Fourier transforms
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• On Discretization of Tori of Compact Simple Lie Groups II
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Cited by in corpus (9)

• Cubature formulas of multivariate polynomials arising from symmetric orbit functions
• Discrete transforms and orthogonal polynomials of (anti)symmetric multivariate cosine functions
• Discrete Fourier transform associated with generalized Schur polynomials
• On E-Discretization of Tori of Compact Simple Lie Groups: II
• Discrete cosine and sine transforms generalized to honeycomb lattice
• Six types of $E-$functions of the Lie groups O(5) and G(2)
• Exact cubature rules for symmetric functions
• Cubature rules for unitary Jacobi ensembles
• Cubature rules from Hall-Littlewood polynomials