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Orbital integrals on unitary hyperbolic spaces over \(\mathfrak p\)-adic fields. (English) Zbl 1404.22023
Summary: For a given étale quadratic algebra \(E\) over a \(\mathfrak{p}\)-adic field \(F\), we establish a transfer of unramified test functions on the symmetric space \(\mathrm{GL}(2,F)\mathrm{GL}(2,E)\) to those on a unitary hyperbolic space so that the orbital integrals match. This is an important step toward a comparison of relative trace formulas of these symmetric spaces, which would yield an example of a non-tempered analogue of a refined global Gross-Prasad conjecture.

22E35 Analysis on \(p\)-adic Lie groups
11F70 Representation-theoretic methods; automorphic representations over local and global fields
22E50 Representations of Lie and linear algebraic groups over local fields
Full Text: DOI Euclid