All Questions

I would like to compute the Hilbert series of the ring of invariants of certain irreducible representations of some groups (namely $SO(5)$ to begin with). To put it in some broader context, let $G$ ...

Let $G$ be a simply connected group over an algebraically closed field $k$, and $I:=\{(g,\gamma)\in G\times G\vert~ g\gamma=\gamma g\}$ the scheme of centralizer. Is $I$ a Cohen-Macaulay scheme ...

Let $G$ be a reductive algebraic group (maybe reductive is not necessary) over an algebraically closed field $k$ of characteristic zero. Let $X$ be a homogeneous affine $G$-variety, i.e. $X=G/K$ for ...