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Results tagged with flag-varieties
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user 9970
6
votes
Accepted
How does the grading on the cohomology of a flag variety break up the regular representation...
I'm unsure if this would be termed a 'simple rule' but perhaps this will be of some use: the Kostka-Foulkes polynomials $K_{\lambda\mu}(q)$ ($\lambda,\mu$ partitions of $n$) determine the change of ba …
- 1,201
3
votes
0
answers
452
views
Flag Varieties via Quiver Varieties
In type $A$ it is possible to realise the flag variety $\mathcal{F}$ of $\text{SL}_{n}(\mathbb{C})$ via Nakajima's quiver varieties: consider the vectors $v=(1,2,\ldots, n-1), w=(0,\ldots,0,n)$. Then, …
- 1,201
3
votes
0
answers
173
views
(semi-)Small resolutions of Peterson varieties
Peterson varieties (in type A) can be described as the subvarieties of the full flag variety
$$\{(F_{i})\;|\; F_{i}\subset \mathbb{C}^{n}, \; \dim F_{i} =i,\; N(F_{i})\subset F_{i+1}\}$$
where $N$ …
- 1,201