Multiplicity equality conjecture for elliptic A-parameters

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

ψ=∑iϕi⊠Sdi\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.

References

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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