Multiplicity one theorem for the Ginzburg–Rallis model: The tempered case

Wan, Chen

doi:10.1090/tran/7690

Multiplicity one theorem for the Ginzburg–Rallis model: The tempered case
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Trans. Amer. Math. Soc. 371 (2019), 7949-7994 Request permission

Abstract:

Following the method developed by Waldspurger and Beuzart-Plessis in their proof of the local Gan–Gross–Prasad conjecture, we prove a local trace formula for the Ginzburg–Rallis model. By applying this trace formula, we prove the multiplicity one theorem for the Ginzburg–Rallis model over the tempered Vogan L-packets. In some cases, we also prove the epsilon dichotomy conjecture which gives a relation between the multiplicity and the exterior cube epsilon factor. This is a sequel to another work of ours in which we proved the geometric side of the trace formula.

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