Completes the 'if' direction of the Boyarchenko-Drinfeld conjecture: unipotent groups over F_q-bar have singleton L-packets precisely when every geometric point lies in the neutral component of its centralizer.
Characters of unipotent groups over finite fields
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Unipotent groups with trivial $\mathbb{L}$-packets are easy
Completes the 'if' direction of the Boyarchenko-Drinfeld conjecture: unipotent groups over F_q-bar have singleton L-packets precisely when every geometric point lies in the neutral component of its centralizer.