. R T / 0 60 45 78 v 1 2 6 A pr 2 00 6 PERMUTATION REPRESENTATIONS ON SCHUBERT VARIETIES
نویسنده
چکیده
This paper defines and studies permutation representations on the equivariant cohomology of Schubert varieties, as representations both over C and over C[t1, t2, . . . , 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 introduced by GoreskyKottwitz-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.
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