Multiplicity equality conjecture for elliptic A-parameters

Let GG be a unitary group or an even orthogonal group, and let

ψ=iϕiSdi\psi=\sum_i \phi_i\boxtimes S_{d_i}

be an elliptic AA-parameter for GG. Let π\pi be an irreducible representation of G(A)G(\mathbb A) such that the LL-parameter of πv\pi_v is ϕψv\phi_{\psi_v} for almost all places vv. Multiplicity equality conjecture. The discrete multiplicity of π\pi equals its predicted multiplicity:

mdisc(π)=m(π).m_{\operatorname{disc}}(\pi)=m(\pi).

This conjecture is formulated to extend the paper's multiplicity formula from generic elliptic AA-parameters to all elliptic AA-parameters, by implying equality in J.-S. Li's inequality. The supplied passage does not state whether it has been proved or remains open.

Sources & referencesView supporting material

Primary source

Rui Chen and Jialiang Zou, “Arthur's multiplicity formula for even orthogonal and unitary groups”, arXiv:2103.07956 (2024).

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