Transfer using Fourier transform and minimal representation of E₇

2025/07/24 by Le, Nhat Hoang, Wang, Bryan Peng Jun
#FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2507.18329

Abstract

In this paper, we study the Sakellaridis-Venkatesh conjecture for the rank-1 spherical variety X=Spin₉\backslash F₄ using an exceptional theta correspondence. We establish the correct transfer map satisfying relative character identities in this case and show that our transfer map agrees with the formula in (Sakellaridis, 2021). Moreover, we show how our techniques lead to a characterization of X-relatively cuspidal representations.

Citations

• Fourier Transform and the minimal representation of E₇
• Relative Langlands Duality
• Strongly tempered hyperspherical Hamiltonian spaces
• Fourier transform on a cone and the minimal representation of even orthogonal group
• Relative character identities and theta correspondence
• Transfer operators and Hankel transforms between relative trace\n formulas, I: character theory
• Transfer operators and Hankel transforms between relative trace\n formulas, II: Rankin-Selberg theory
• Relative functoriality and functional equations via trace formulas
• Plancherel decomposition of Howe duality and Euler factorization of automorphic functionals
• Periods and harmonic analysis on spherical varieties
• A Conjecture of Sakellaridis-Venkatesh on the Unitary Spectrum of Spherical Varieties
• Spherical functions on spherical varieties
• Subrepresentation Theorem for p-adic Symmetric Spaces
• An order-reversing duality map for conjugacy classes in Lusztig's canonical quotient
• An order-reversing duality map for conjugacy classes in Lusztig's canonical quotient
• Explicit Hilbert spaces for certain unipotent representations III

Cited by

• Fourier Transform and the minimal representation of E₇

Related

• Relative character identities and theta correspondence
• Duality for spherical representations in exceptional theta\n correspondences
• A Conjecture of Sakellaridis-Venkatesh on the Unitary Spectrum of Spherical Varieties
• Fundamental Lemma for Rank One Spherical Varieties of Classical Types
• On Representations of Weyl Groups attached to Spherical Varieties