6 problems

Integral Borel basis conjecture. The elements $E_AH_B$ with $A\in{\mathbb N}^{\Phi^+}$, $B\in{\mathbb N}_{i_0}^n$, and $|A|+|B|\le d$ form an $\mathcal A$-basis of…

Let $C$ be a triangular right coideal subalgebra of the form … Here $w_+,w_-\in W$, $\phi_+$ and $\phi_-$ are characters, $L$ is the associated lattice, $S$ is the antipode, and…

Completeness conjecture. The constructed examples are all Borel subalgebras of

Triangularity conjecture. Every Borel subalgebra is triangular.

Classification conjecture. The algebra $C$ is a Borel subalgebra if and only if

Let $\mathfrak{g}=W_n$ be the Jacobson–Witt algebra of rank $n$ over the field $\mathbb{F}$, where $W_n$ is the derivation algebra of…