Graham, William Positivity in equivariant Schubert calculus. (English) Zbl 1069.14055 Duke Math. J. 109, No. 3, 599-614 (2001). Summary: We prove a positivity property for the cup product in the \(T\)-equivariant cohomology of the flag variety. This was conjectured by D. Peterson and has as a consequence a conjecture of S. Billey [Duke Math. J. 96, No.1, 205–224 (1999; Zbl 0980.22018)]. The result for the flag variety follows from a more general result about algebraic varieties with an action of a solvable linear algebraic group such that the unipotent radical acts with finitely many orbits. The methods are those used by S. Kumar and M. Nori [Int. Math. Res. Not. 1998, No.14, 757–763 (1998; Zbl 1014.17023)]. Cited in 8 ReviewsCited in 56 Documents MSC: 14M17 Homogeneous spaces and generalizations 14C17 Intersection theory, characteristic classes, intersection multiplicities in algebraic geometry 14F43 Other algebro-geometric (co)homologies (e.g., intersection, equivariant, Lawson, Deligne (co)homologies) 14M15 Grassmannians, Schubert varieties, flag manifolds 17B37 Quantum groups (quantized enveloping algebras) and related deformations Citations:Zbl 1014.17023; Zbl 0980.22018 × Cite Format Result Cite Review PDF Full Text: DOI arXiv