Abstract
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 $\mathrm{GL}(2,F)\backslash\mathrm{GL}(2,E)$ 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.
Citation
Masao TSUZUKI. "Orbital Integrals on Unitary Hyperbolic Spaces Over $\frak p$-adic Fields." Tokyo J. Math. 39 (3) 923 - 975, March 2017. https://doi.org/10.3836/tjm/1491465736