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Results tagged with lie-groups
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user 16002
Lie Groups are Groups that are additionally smooth manifolds such that the multiplication and the inverse maps are smooth.
2
votes
Accepted
Chains in $K\backslash G/B$ lying over a closed $K$-orbit
Malheureusement, this is not true, not even for the weak order. This can be seen for example when $G = GL(4)$ and $K = GL(2) \times GL(2)$. Then $K \backslash G / B$ is parameterized by involutions …
- 1,780
6
votes
Cohomology ring of a flag variety and representation theory
Both the study of ordinary Schubert calculus (the ordinary, e.g. Borel-Moore, cohomology of Schubert varieties of the flag variety) and the study of Kazhdan-Lusztig theory (the intersection cohomology …
- 1,780
2
votes
Covering relations in $K\backslash G/B$
While the paper of Richardson-Springer does study the weak order, it also has useful results on the usual (strong) Bruhat order. In particular, Theorem 7.11 says that Bruhat order is characterized as …
- 1,780
2
votes
Bruhat order and Schubert cycles
The result is stated and proved as Corollary 2.2.2 of Michel Brion's Lectures on the Geometry of Flag Varieties.
- 1,780
5
votes
Cohomology Ring of the Flag Manifolds, Cartan Subalgebras, and Weyl Groups
(1) Assuming you are referring to the coefficient field for your cohomology theory, then yes, the result immediately extends to $\mathbb{R}$ and $\mathbb{C}$ coefficients.
(2) Two sources are Fulton' …
- 1,780
10
votes
Accepted
Is there a geometric interpretation of skew Schur functions?
This is discussed in Stanley's paper Some combinatorial aspects of the Schubert calculus. Corollary 3.7 says that under the natural isomorphism given by the Borel presentation of $H^*(G/P)$ which send …
- 1,780