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Let $G=\mathrm{Gl}_n(\mathbb C)$ and $V$ an irreducible $G$-module on which $G$ acts polynomially. In other words, the algebraic group action of $G$ on the affine space $V$ extends to an algebraic ...

How is the cohomology of Bott-Samelson varieties (desingularizations of Schubert Varieties ) usually calculated? Let's fix the Lie group to be $GL_n(\mathbb{C})$ or $SL_n(\mathbb{C})$ here. Is there ...

Let $G$ be a connected reductive group over an algebraically closed field. Let $T$ be a maximal torus and $x\in T$. Let $G_x$ denote the centraliser of $x$ in $G$. Question: What is an explicit ...

In this question, the following fact was used by the respondent A Zariski-closed subset of a compact Lie group $G$ with nonzero Haar measure contains a coset of $G^0$, the connected component of $G$ ...

Let $G$ be a complex linear algebraic group acting on a smooth complex projective variety $X$ with finitely many orbits. Note that each $G$-orbit is a smooth locally closed subvariety of $X$. For a ...