Questions tagged [flags]
The flags tag has no usage guidance.
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B-invariant subvarieties
Let $B$ be a connected, solvable algebraic group (of dimension 2) acting on a projective variety $Y$ (of dimension $3$): for instance, let $B$ be a Borel subgroup of a reductive algebraic group $G$.
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Tautological and normal bundles over flag manifolds and jet bundles
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 $G(V,k,l)$ and the two ...
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Request for info on the space of commuting matrices preserving a flag.
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 Vi), and
B strictly ...
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Why do flag manifolds, in the P(V_rho) embedding, look like products of P^1s?
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 vector $\rho$ equal to ...
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Defining Equations of a Flag Variety
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's Plucker relations,...
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Do Richardson varieties have rational singularities in arbitrary characteristic?
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 $v \leq w$ be elements of ...
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simplicial deRham complex and model category structure
To every simplicial manifold is associated its simplicial deRham complex.
Is there any literature that discusses explicitly to which extent this classical construction, regarded as a (contravariant) ...
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Why is the Nil-Hecke Algebra appearing?
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 difference ...
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When should a moment polytope have "smooth" faces?
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 only orbifold ...
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Flag Varieties - Projective Curves
Is it true that there are no projective curves which are also flag manifolds? If so, why?
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