4 problems

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The central-commutator nilpotence conjecture for two endomorphisms
Central-commutator nilpotence conjecture. Then
Conjectureopendrinfeld-sokolov-hierarchies lie-algebras nilpotencearXiv posted 2 days ago
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Nonlinearizability conjecture for non-ADE Drinfeld–Sokolov hierarchies
Nonlinearizability conjecture. The functions $O_k$ with $k\geq 1$ may not vanish; equivalently, the Virasoro symmetries for Drinfeld–Sokolov hierarchies of non-ADE type are not lin…
Conjectureopendrinfeld-sokolov-hierarchies tau-functions virasoro-symmetriesarXiv posted 2 days ago
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Dubrovin–Zhang's conjecture for ADE Drinfeld–Sokolov hierarchies
Dubrovin–Zhang's conjecture. All Drinfeld–Sokolov hierarchies of ADE type satisfy (A1)–(A3).
Conjectureopendrinfeld-sokolov-hierarchies integrable-systems virasoro-algebraarXiv posted 2 days ago
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Conjecture on fourth-order Painlevé systems from type I hierarchies
The type I hierarchies are the Drinfeld–Sokolov hierarchies associated with the regular conjugacy classes of the finite Weyl group $W(A_n)$ , corresponding to partitions of the form…
Conjectureopenaffine-lie-algebras drinfeld-sokolov-hierarchies painleve-equationsarXiv posted 2 days ago

The central-commutator nilpotence conjecture for two endomorphisms