I've been reading Fulton's Young Tableaux, and I'm trying to understand flag varieties. I want to understand the defining equations of a Flag Variety, but the coordinates in Fulton …

Hello! Recently, doing my research on jet bundles, I was led to consider the following construction. Let $V$ be a real vector space of dimension $n$. Consider the flag manifold …

The title basically asks the question. I'll review the relevant terminology and explain what I have and haven't found in the literature. Let $G$ be a reductive group. Let $v \leq …

To every simplicial manifold is associated its simplicial deRham complex. Is there any literature that discusses explicitly to which extent this classical construction, regarded a …

The Nil-Hecke algebra is defined to be the subalgebra of the endomorphism ring of $\mathbb{C}[x_1,\ldots,x_n]$ generated by the operators of multiplication by $x_i$ and the divided …

A codimension $d$ face of a polytope is called rationally smooth if it lies on only $d$ facets, because this is exactly the condition for the corresponding toric variety to have on …

Bert Kostant mentioned an odd fact to me some time ago. As usual (with such statements), fix a complex, connected, reductive) Lie group $G$, with maximal torus $T$, and Weyl vecto …

Is it true that there are no projective curves which are also flag manifolds? If so, why?

Fix a flag of subspaces V1 in V2 in V3, etc. all in Cn. Consider the space of pairs of commuting linear transformations A and B such that: A preserves the flag (i.e. A(Vi) is in V …