let's consider the example of the big bruhat cell for the flag variety of pgl(3). this is the image of the map
str upper tri -> str upper unipotent -> cosets(lower tri)
where the first arrow is exponentiation and the second is... almost obvious, but we're going to have to be somewhat careful here...
and then we're going to be interested in limiting behavior...
let me try again...
we're interested in the decomposition of g/k wrt a certain "observer" subgp h (secretly the stabilizer borel of the favorite total flag). we have certain representatives in g/k of the components, i guess.
actually, how are we going to get those representatives in our example?? what we actually seem to have so far is the conjugate stabilizer subalgebras of those representatives...
i guess actually it should be ok; officially the weyl group is defined as special cosets of the cartan... or something like that... hmm, still need to work this out...
No comments:
Post a Comment