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October 8, 2025Open Access

Fourier Transform and the minimal representation of E₇

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Authors

WGWee Teck GanNGNadya Gurevich

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Overview

This paper studies the representation of E7 in p-adic fields, highlighting connections to integral operators and Fourier transforms.

Key Points

  • The paper explores the minimal representation of the split group E7 over a p-adic field, revealing its intricate structure.
  • A unique integral operator, related to the Fourier transform on a 17-dimensional cone, acts geometrically on this representation.
  • Formulas for the action of involutive elements conjugating parabolic subgroups are derived, enhancing understanding of representation theory.
  • Connections to generalized Fourier transforms, as defined by Braverman and Kazhdan, are established, suggesting broader implications.

Cite This Study

Gan et al. (2025) studied this question.

synapsesocial.com/papers/68e6494525bc5bdb98713affhttps://doi.org/10.48550/arxiv.2507.16968
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