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• W1903180429 abstract "This survey paper describes two geometric representations of the permutation group using the tools of toric topology. These actions are extremely useful for computational problems in Schubert calculus. The (torus) equivariant cohomology of the flag variety is constructed using the combinatorial description of Goresky-Kottwitz-MacPherson, discussed in detail. Two permutation representations on equivariant and ordinary cohomology are identified in terms of irreducible representations of the permutation group. We show how to use the permutation actions to construct divided difference operators and to give formulas for some localizations of certain equivariant classes. This paper includes several new results, in particular a new proof of the Chevalley-Monk formula and a proof that one of the natural permutation representations on the equivariant cohomology of the flag variety is the regular representation. Many examples, exercises, and open questions are provided." @default.
• W1903180429 created "2016-06-24" @default.
• W1903180429 creator A5037445253 @default.
• W1903180429 date "2007-06-04" @default.
• W1903180429 modified "2023-09-27" @default.
• W1903180429 title "Permutation actions on equivariant cohomology" @default.
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