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Assume we work over an algebraically closed field of characteristic zero. I know that for a connected semisimple algebraic group there is an upper bound for the number of isomorphism classes of ...

Let $G$ be a connected simple reductive group over $\mathbb C$. Let $V$ be a finite-dimensional complex representation of $G$. Given a vector $v \in V$, it is natural to consider its stabilizer group $...

Let $V$ be a real vector space (of finite dimension) and let $G$ be a unipotent Lie subgroup of $\mathrm{GL}(V)$. The orbits of points under the action of $G$ (that is, the sets $Gx = \{T(x) \ : \ T \...