A Local Relative Trace Formula for the Ginzburg-Rallis Model: the Geometric Side

2016/08/12 by Wan, Chen
#22E35 #22E50 (Primary) #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1608.03837

Abstract

Following the method developed by Waldspurger and Beuzart-Plessis in their proofs of the local Gan-Gross-Prasad conjecture, we are able to prove the geometric side of a local relative trace formula for the Ginzburg-Rallis model. Then by applying such formula, we prove a multiplicity formula of the Ginzburg-Rallis model for the supercuspidal representations. Using that multiplicity formula, we prove the multiplicity one theorem for the Ginzburg-Rallis model over Vogan packets in the supercuspidal case.

Related

• Multiplicity One Theorem for the Ginzburg-Rallis Model: the tempered case
• The multiplicity problems for the unitary Ginzburg-Rallis models
• The local twisted Gan-Gross-Prasad conjecture for GL(V)/U(V)
• Multiplicity formula for induced representations: Bessel and Fourier-Jacobi models over Archimedean local fields
• The local Gan-Gross-Prasad conjecture for U(n+1) × U(n) : a non-generic case