Geometric side of a local relative trace formula

Delorme, P.; Harinck, P.; Souaifi, S.

doi:10.1090/tran/7360

Geometric side of a local relative trace formula
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by P. Delorme, P. Harinck and S. Souaifi PDF

Trans. Amer. Math. Soc. 371 (2019), 1815-1857 Request permission

Abstract:

Following a scheme suggested by B. Feigon, we investigate a local relative trace formula in the situation of a reductive $p$-adic group $G$ relative to a symmetric subgroup $H= \underline {H}(\mathrm {F})$ where $\underline {H}$ is split over the local field $\mathrm {F}$ of characteristic zero and $G = \underline {G} (\mathrm {F})$ is the restriction of scalars of $\underline {H} _{/\mathrm {E}}$ relative to a quadratic unramified extension $\mathrm {E}$ of $\mathrm {F}$. We adapt techniques of the proof of the local trace formula by J. Arthur in order to get a geometric expansion of the integral over $H \times H$ of a truncated kernel associated to the regular representation of $G$.

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