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 38m revised Why the orbit is of dimension $12$? deleted 16 characters in body 11h revised How to show that each tangent vector to $\mathbb{R}^n$ at a point $a$ is of the form $\xi(f) = \sum_{i} c_i \frac{\partial f}{\partial x_i}(a)$? added 171 characters in body 12h revised How to show that each tangent vector to $\mathbb{R}^n$ at a point $a$ is of the form $\xi(f) = \sum_{i} c_i \frac{\partial f}{\partial x_i}(a)$? added 467 characters in body 2d asked How to show that each tangent vector to $\mathbb{R}^n$ at a point $a$ is of the form $\xi(f) = \sum_{i} c_i \frac{\partial f}{\partial x_i}(a)$? Apr19 awarded Yearling Apr18 asked Questions about strata of a variety: the nilpotent cone of $\mathfrak{sl}_2$. Apr17 accepted Why Demazure operator is an endomorphism of $\mathbb{Z}[P]$? Apr15 comment Why the orbit is of dimension $12$? thank you very much. Apr15 comment Why the orbit is of dimension $12$? thank you very much. I think that for vector spaces we have $\dim V/W = \dim V - \dim W$, where $W$ is a subspace of $V$. But it seems that for groups, we have $[G: H]=|G|/|H|$, where $H$ is a subgroup of $G$. Apr14 asked How to compute perverse sheaves? Apr14 comment Why Demazure operator is an endomorphism of $\mathbb{Z}[P]$? @JyrkiLahtonen, now I understand. Thank you very much. Apr14 comment Why Demazure operator is an endomorphism of $\mathbb{Z}[P]$? @JyrkiLahtonen, thank you very much. Usually, weights are linear combinations of roots. Why $e^{\alpha}$ is also a weight? Here $\alpha$ is a root. Apr14 comment Why Demazure operator is an endomorphism of $\mathbb{Z}[P]$? @JyrkiLahtonen, thank you very much. Why elements in $\mathbb{Z}[P]$ is of the form $e^{k \alpha}$? I know that $s_{\alpha_i}$ ($\alpha_i$ is a simple root) is a simple reflection. How do we define $s_{\alpha}$ when $\alpha$ is not a simple root? Why $s_{\alpha} \cdot u = s_{\alpha}(u + \rho) - \rho = e^{-k\alpha}$? Apr14 asked Why Demazure operator is an endomorphism of $\mathbb{Z}[P]$? Apr14 comment Why the orbit is of dimension $12$? thank you very much. Why the dimension of the orbit is not $8/2=4$ but $8-2=6$? Apr11 accepted Why the orbit is of dimension $12$? Apr11 asked Why the orbit is of dimension $12$? Apr11 asked How to understand the algebra $U_A(Lg)$? Apr10 awarded Nice Question Apr5 revised Question about Poincare duality and homology of a cylinder. added 1 character in body