Permutation representations on Schubert varieties

Julianna S. Tymoczko
2008 American Journal of Mathematics  
This paper defines and studies permutation representations on the equivariant cohomology of Schubert varieties, as representations both over C and over C[t 1 , t 2 , . . . , tn]. We show these group actions are the same as an action studied geometrically by M. Brion, and give topological meaning to the divided difference operators studied by Berstein-Gelfand-Gelfand, Demazure, Kostant-Kumar, and others. We analyze these representations using the combinatorial approach to equivariant cohomology
more » ... variant cohomology introduced by Goresky-Kottwitz-MacPherson. We find that each permutation representation on equivariant cohomology produces a representation on ordinary cohomology that is trivial, though the equivariant representation is not.
doi:10.1353/ajm.0.0018 fatcat:rtbnnxv37zamjkkpvf363thniq