Duke Mathematical Journal

Positivity in equivariant Schubert calculus

William Graham

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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. 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.

Article information

Duke Math. J., Volume 109, Number 3 (2001), 599-614.

First available in Project Euclid: 5 August 2004

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 14M17: Homogeneous spaces and generalizations [See also 32M10, 53C30, 57T15]
Secondary: 14C17: Intersection theory, characteristic classes, intersection multiplicities [See also 13H15] 14F43: Other algebro-geometric (co)homologies (e.g., intersection, equivariant, Lawson, Deligne (co)homologies) 14M15: Grassmannians, Schubert varieties, flag manifolds [See also 32M10, 51M35] 17B37: Quantum groups (quantized enveloping algebras) and related deformations [See also 16T20, 20G42, 81R50, 82B23]


Graham, William. Positivity in equivariant Schubert calculus. Duke Math. J. 109 (2001), no. 3, 599--614. doi:10.1215/S0012-7094-01-10935-6. https://projecteuclid.org/euclid.dmj/1091737323

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