Dear mathematicians, recently I asked a question on mo, but didn't get much attention. Here the link to the question: mathoverflow.net/questions/219650/…
The point which is still unclear to me, and left open in the answer I gave myself, is the following: given the parametrization of Schubert varieties as in the question, I would like to know which isotropic subspaces are parametrized in terms of the partition.
The references cited in the question of course give a (quite complucated) answer, but their formulas do not match well with my notation and my parametrization.
Please keep in mind, that by a Schubert variety I mean the closure of BwP/P for some Weyl group element w, i.e. I want to use B instead of B^-
Concerning the paper of Tamvakis, page 19, I don't really understand why the embedding \varphi from W=the Weyl group to S_2p=the symmetric group on 2p letters in the way it is given there reflects the isomorphism between W=thought as barred permutations of p letters and W=thought as the normalizer N_G(T) divided by the torus T, i.e. why the permutations in the
image give us the "right" matrices. (I guess there is a choice of basis - called standard basis - involved in the business, so that the matrix of the quadratic form Q is of the form with ones on the second diagonal.)
