# Tagged Questions

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### What's the relation of the Hecke algebra of a pair and the flag variety?

Let $G$ be a real semisimple Lie group and $K$ a maximal compact subgroup. Let $\mathfrak{g}$ and $\mathfrak{k}$ be the complexified Lie algebra of $G$ and $K$, respectively. Then the Hecke algebra ...
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### Flags of varieties

I was wondering if there is a generalization of flags in the following way: Suppose you have a series of inclusions of affine varieties $V_1\hookrightarrow V_2\hookrightarrow\cdots\hookrightarrow V_n$ ...
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### On the maximal powers of $q$ which arise in a quantum product

Let $X=G/P$ be a generalized flag variety (where $G$ denotes a connected, simply connected, semisimple complex linear algebraic group and $P$ a parabolic subgroup). In this paper by Fulton and ...
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### Schubert Calculus for the Full Flags

Almost all introductory texts on Schubert calculus discuss the Grassmannian case only. Does there exist a nice discussion of the full flag manifold case $SU(N)/T^{N-1}$? A low dimensional example ...
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### Pullback of a sheaf associated to a divisor

I am reading a paper Desingularisation des varietes de Schubert generalisees by Demazure. I am interested in Lemma 3 on page 58. In particular, I would like to know whether the lemma is true and how ...
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### Equivariant $K$-theory, singular vectors, and flag manifolds

For a homogeneous space $M = G/B$, with $G$ a (complex) semi-simple Lie group, it is very well-known that equivariant vector bundles $E$ over $M$ correspond to representations $(V_{\lambda},\lambda)$ ...
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### Weight decomposition and eigenspaces Euler vector field

Let $V$ be a finite dimensional vector space over $\mathbb{C}$, denote $V^{\times} = V -0$ and let $\pi : V^{\times} \rightarrow \mathbb{P}(V)$ be the quotient by the natural action of ...