Beyond the Adams Conjecture

Alexander Hazeltine; Aarya Kumar; Andrew Tung

Beyond the Adams Conjecture

Representation Theory 2026-07-26 v1 Number Theory

Authors: Alexander Hazeltine , Aarya Kumar , Andrew Tung

Abstract

For symplectic and even orthogonal groups over a $p$ -adic field, we determine the number of local Arthur packets containing the local theta lift of a tempered representation at the first occurrence in the going-up tower. These counts show that the local theta lifts may lie in many more local Arthur packets than those predicted by the Adams conjecture.

Cite

@article{arxiv.2607.23885,
  title  = {Beyond the Adams Conjecture},
  author = {Alexander Hazeltine and Aarya Kumar and Andrew Tung},
  journal= {arXiv preprint arXiv:2607.23885},
  year   = {2026}
}