The local converse theorem establishes local gamma factors and theta correspondence in irreducible automorphic representations of Sp2n.
In this paper, we establish the local converse theorem and the stability of local gamma factors for Sp₂ₙ Sp ~ 2 n via the precise local theta correspondence between Sp₂ₙ Sp ~ 2 n and SO₂ₙ₊₁ SO 2 n + 1 over local fields of characteristic not equal to 2. We also prove the rigidity theorem for irreducible generic cuspidal automorphic representations of Sp₂ₙ Sp ~ 2 n over number fields.
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Haan et al. (2025) studied this question.
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