Positivity of Peterson Schubert calculus

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dc.contributor.authorGoldin, Rebeccaen
dc.contributor.authorMihalcea, Leonardoen
dc.contributor.authorSingh, Rahulen
dc.date.accessioned2025-02-04T13:28:15Zen
dc.date.available2025-02-04T13:28:15Zen
dc.date.issued2024-10en
dc.description.abstractThe Peterson variety is a subvariety of the flag manifold G/B equipped with an action of a one-dimensional torus, and a torus invariant paving by affine cells, called Peterson cells. We prove that the equivariant pull-backs of Schubert classes indexed by arbitrary Coxeter elements are dual (up to an intersection multiplicity) to the fundamental classes of Peterson cell closures. Dividing these classes by the intersection multiplicities yields a Z-basis for the equivariant cohomology of the Peterson variety. We prove several properties of this basis, including a Graham positivity property for its structure constants, and stability with respect to inclusion in a larger Peterson variety. We also find formulae for intersection multiplicities with Peterson classes. This explains geometrically, in arbitrary Lie type, recent positivity statements proved in type A by Goldin and Gorbutt.en
dc.description.versionAccepted versionen
dc.format.extent34 page(s)en
dc.format.mimetypeapplication/pdfen
dc.identifierARTN 109879 (Article number)en
dc.identifier.doihttps://doi.org/10.1016/j.aim.2024.109879en
dc.identifier.eissn1090-2082en
dc.identifier.issn0001-8708en
dc.identifier.orcidMihalcea, Constantin [0000-0002-8437-9163]en
dc.identifier.urihttps://hdl.handle.net/10919/124477en
dc.identifier.volume455en
dc.language.isoenen
dc.publisherElsevieren
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subjectPeterson varietiesen
dc.subjectEquivariant cohomologyen
dc.subjectPositivityen
dc.titlePositivity of Peterson Schubert calculusen
dc.title.serialAdvances in Mathematicsen
dc.typeArticle - Refereeden
dc.type.dcmitypeTexten
dc.type.otherArticleen
dc.type.otherJournalen
pubs.organisational-groupVirginia Techen
pubs.organisational-groupVirginia Tech/Scienceen
pubs.organisational-groupVirginia Tech/Science/Mathematicsen
pubs.organisational-groupVirginia Tech/All T&R Facultyen
pubs.organisational-groupVirginia Tech/Science/COS T&R Facultyen

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