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arXiv · 2507.16968

Fourier Transform and the minimal representation of $E_7$

Wee Teck Gan·Nadya Gurevich
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Abstract

We consider the minimal representation of the adjoint split group $E_7$ over a p-adic field. The representation has a model in a space of functions on a 17 dimensional cone $\Omega$, and elements of the unique parabolic subgroup Q with abelian radical act by simple geometric formulas. We write a formula for the action of an involutive element $s$, conjugating $Q$ to the opposite parabolic $\bar Q$. The resulting integral operator, called a Fourier transform on $\Omega$, is related to generalized Fourier transform, defined by Braverman and Kazhdan.

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Wee Teck Gan, Nadya Gurevich. 2025-07-22. Fourier Transform and the minimal representation of $E_7$. https://arxiv.org/abs/2507.16968

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