16
votes
2answers
955 views

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 ...
1
vote
1answer
230 views

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 ...