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Results tagged with flag-varieties
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user 4231
8
votes
Hecke algebra and $H^*(G/B)$
The early work of Borel showed in effect how to interpret the cohomology algebra of a flag variety as the coinvariant algebra associated to the Weyl group, which affords the regular representation of …
- 52.9k
5
votes
Automorphism group of flag manifolds?
While the question and answers have explained different aspects of the story for complex groups and homogeneous spaces, it might be worthwhile to place the question in a broader context. The complex …
- 52.9k
4
votes
Computing relative Lie algebra cohomology (as appears in Borel-Weil-Bott theorem)
The theorems of Borel-Weil and then Bott, along with Kostant's translation of the ideas into the language of Lie algebra cohomology, do much to illuminate classical representation theory (Cartan-Weyl) …
- 52.9k
4
votes
What is the significance that the Springer resolution is a moment map?
The short answer might be that this viewpoint provides an attractive alternative way to construct the Springer resolution as a special case in a broader geometric framework, following ideas of Kostant …
- 52.9k
9
votes
Accepted
The anticanonical bundle on a flag variety is ample
It's worth pointing out that the criterion for ampleness applies uniformly for reductive groups and flag varieties in any characteristic. From the algebraic group viewpoint, the only subtle point is …
- 52.9k
65
votes
6
answers
9k
views
Origin of terms "flag", "flag manifold", "flag variety"?
These terms have become common in Lie theory and related algebraic geometry and combinatorics, as seen in many questions posted on MO, but it's unclear to me where they first came into use. Probably …
- 52.9k
39
votes
Accepted
Rep Theory Consequences of Bott--Weil--Borel
It's always a good idea to ask (as students typically do) why one is studying a particular subject or theorem. Here are some of my views, from the algebraic side of representation theory:
1) The or …
- 52.9k