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Abstract We construct a novel family of difference-permutation operators and prove that they are diagonalized by the wreath MacdonaldP-polynomials; the eigenvalues are written in terms of elementary symmetric polynomials of arbitrary degree. Our operators arise from integral formulas for the action of the horizontal Heisenberg subalgebra in the vertex representation of the corresponding quantum toroidal algebra. 

The Keck Planet Finder (KPF) is a fiber-fed, high-resolution, echelle spectrometer that specializes in the discovery and characterization of exoplanets using Doppler spectroscopy. In designing KPF, the guiding principles were high throughput to promote survey speed and access to faint targets, and high stability to keep uncalibrated systematic Doppler measurement errors below 30 cm s−1. KPF achieves optical illumination stability with a tip-tilt injection system, octagonal cross-section optical fibers, a double scrambler, and active fiber agitation. The optical bench and optics with integral mounts are made of Zerodur to provide thermo-mechanical stability. The spectrometer includes a slicer to reformat the optical input, green and red channels (445-600 nm and 600-870 nm), and achieves a resolving power of ∼97,000. Additional subsystems include a separate, medium-resolution UV spectrometer (383-402 nm) to record the Ca II H & K lines, an exposure meter for real-time flux monitoring, a solar feed for sunlight injection, and a calibration system with a laser frequency comb and etalon for wavelength calibration. KPF was installed and commissioned at the W. M. Keck Observatory in late 2022 and early 2023 and is now in regular use for scientific observations. This paper presents an overview of the as-built KPF instrument and its subsystems, design considerations, and initial on-sky performance.