5 problems

Let $\frak m$ be the Monster Lie algebra, and let $\scr V$ and $\scr V'$ be the $(\frak g\frak l_2,M)$-modules identified inside $\frak m$. For $v\in\scr V$ or $v\in\scr V'$, write…

Amalgam conjecture. The group $G(\mathfrak m)$ arises naturally as an amalgam of the $\operatorname{GL}_2$ subgroups and pro-unipotent subgroups discussed in the preceding construc…

Amalgam conjecture. The group $G(\mathfrak m)$ is an amalgam of automorphism groups of Lie algebras related to $\mathfrak m$.

Dense embedding conjecture. The subgroup $U^+$ embeds as a dense subgroup of $\widehat{U}^+$.

Let $\mathfrak{m}$ be the Monster Lie algebra, and for each $j>0$ let $\mathcal{G}_j$ denote the set of $\mathfrak{gl}_2$ subalgebras associated with the imaginary simple root…