show/hide this revision's text 2 clarified so as not to unintentionally put down the L-S paper

Vic Reiner, Alex Yong, and I spell this out in Sections 4.1 and 4.2 of our paper on the cohomology rings of Schubert varieties: http://arxiv.org/abs/0809.2981

This is not really original to us: for type A we refer back to Lascoux and Schutzenberger's paper Trellis et bases des groupes de Coxeter, Elect J. Combin. 3, no. 2 R27, though perhaps they don't state things quite as nicelyexactly in this form.

Note for Allen: The rest of our paper might not be as irrelevant to you as it might seem at first glance. Jim Carrell started a line of work back in the 80s relating cohomology rings of Schubert varieties to their local equations at the identity. Interestingly, their strongest results are only for type A.
show/hide this revision's text 1

Vic Reiner, Alex Yong, and I spell this out in Sections 4.1 and 4.2 of our paper on the cohomology rings of Schubert varieties: http://arxiv.org/abs/0809.2981

This is not really original to us: for type A we refer back to Lascoux and Schutzenberger's paper Trellis et bases des groupes de Coxeter, Elect J. Combin. 3, no. 2 R27, though perhaps they don't state things quite as nicely.

Note for Allen: The rest of our paper might not be as irrelevant to you as it might seem at first glance. Jim Carrell started a line of work back in the 80s relating cohomology rings of Schubert varieties to their local equations at the identity. Interestingly, their strongest results are only for type A.