2 problems

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Kirillov's conjecture on Kirillov functions for unitriangular groups
Kirillov's conjecture. These Kirillov functions comprise all the irreducible characters of $\mathrm{UT}_n(q)$ if and only if $n\leq 12$ . The paper notes that the assertion is known…
Conjecturerefutedkirillov-orbit-method representation-theory unitriangular-groupsarXiv posted 2 days ago
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Conjecture on exponential Kirillov functions for unitriangular groups
Exponential Kirillov-function conjecture. The irreducible characters and exponential Kirillov functions of $\mathrm{UT}_n(q)$ coincide if and only if $n\leq 6p$ .
Conjectureopenkirillov-orbit-method representation-theory unitriangular-groupsarXiv posted 2 days ago

Kirillov's conjecture on Kirillov functions for unitriangular groups