The Gromov-Witten instanton expansion of the 4D N=2 prepotential is reinterpreted as a spectral decomposition into eigenfunctions of a Laplace-Beltrami operator on the Coxeter quotient of the moduli space, explaining the natural appearance of Bessel and theta functions for dihedral groups.
Barban¸ con, Finite Reflection Groups: Invariant functions and functions of the Invariants in finite class of differentiability (2019), arXiv:1906.06494 [math.FA]
2 Pith papers cite this work. Polarity classification is still indexing.
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abstract
Let $W$ be a finite reflection group. A $W$-invariant function of class~$C^{\infty}$ may be expressed as a functions of class $C^{\infty}$ of the basic invariants. In finite class of differentiability, the situation is not this simple. Let~$h$ be the greatest Coxeter number of the irreducible components of $W$ and $P$ be~the Chevalley mapping, if $f$ is an invariant function of class $C^{hr}$, and $F$ is the function of invariants associated by $f=F\circ P$, then $F$ is of class $C^r$. However if~$F$ is of class $C^r$, in general $f=F\circ P$ is of class $C^r$ and not of class $C^{hr}$. Here we determine the space of $W$-invariant functions that may be written as functions of class $C^r$ of the polynomial invariants and the subspace of functions $F$ of class $C^r$ of the invariants such that the invariant function $f=F\circ P$ is of class $C^{hr}$.
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hep-th 2years
2026 2verdicts
UNVERDICTED 2representative citing papers
Coxeter symmetries from isomorphic flops in Kähler-favorable CICYs make the 4D N=2 prepotential solve the Helmholtz equation on the moduli space, enabling resummed expressions from worldsheet instantons.
citing papers explorer
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Harmonic Analysis of the Instanton Prepotential
The Gromov-Witten instanton expansion of the 4D N=2 prepotential is reinterpreted as a spectral decomposition into eigenfunctions of a Laplace-Beltrami operator on the Coxeter quotient of the moduli space, explaining the natural appearance of Bessel and theta functions for dihedral groups.
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Kaleidoscopes, Waves and the Prepotential
Coxeter symmetries from isomorphic flops in Kähler-favorable CICYs make the 4D N=2 prepotential solve the Helmholtz equation on the moduli space, enabling resummed expressions from worldsheet instantons.