5 problems

Let $G$ be a real reductive group, let $P$ be a parabolic subgroup with nilpotent Lie algebra $\mathfrak{n}$, and let $\pi$ be a Casselman–Wallach representation of $G$. Write…

Let $r\in\mathbb{N}$, and let $\Phi^1[r+2,r]$ be the $\mathfrak{S}_{r+2}\times\mathfrak{S}_r$-module appearing in the relative polynomial-degree-$2$ Lie algebra homology calculatio…

Let $V$ be a finite-dimensional vector space, let $\operatorname{Jord}(V)$ be the free Jordan algebra generated by $V$, and let $\mathsf{TAG}(\operatorname{Jord}(V))$ be its functo…

Let $J(r)$ be the free Jordan algebra of rank $r$, and let $\mathfrak{sl}_2(J(r))$ be its universal central extension of the Tits–Kantor–Koecher algebra. The Lie algebra…

Let $X$ be an affine algebraic manifold, let ${\mathcal T}_X$ be its Lie algebra of algebraic vector fields, and let $\mathfrak h\subseteq {\mathcal T}_X$ be a Lie subalgebra of fi…