Back stable Schubert calculus

Simple item page
dc.contributor.authorLam, Thomasen
dc.contributor.authorLee, Seung Jinen
dc.contributor.authorShimozono, Mark M.en
dc.contributor.departmentMathematicsen
dc.date.accessioned2021-07-29T18:06:01Zen
dc.date.available2021-07-29T18:06:01Zen
dc.date.issued2021-05en
dc.description.abstractWe study the back stable Schubert calculus of the infinite flag variety. Our main results are: - a formula for back stable (double) Schubert classes expressing them in terms of a symmetric function part and a finite part; - a novel definition of double and triple Stanley symmetric functions; - a proof of the positivity of double Edelman-Greene coefficients generalizing the results of Edelman-Greene and Lascoux-Schutzenberger; - the definition of a new class of bumpless pipedreams, giving new formulae for double Schubert polynomials, back stable double Schubert polynomials, and a new form of the Edelman-Greene insertion algorithm; - the construction of the Peterson subalgebra of the infinite nilHecke algebra, extending work of Peterson in the affine case; - equivariant Pieri rules for the homology of the infinite Grassmannian; - homology divided difference operators that create the equivariant homology Schubert classes of the infinite Grassmannian.en
dc.description.notesT.L. was supported by NSF DMS-1464693. S. J. Lee was supported by the National Research Foundation of Korea (NRF) grant funded by the Korean government (MSIT) (No. 2019R1C1C1003473). M.S. was supported by NSF DMS-1600653.en
dc.description.sponsorshipNSFNational Science Foundation (NSF) [DMS-1464693, DMS-1600653]; National Research Foundation of Korea (NRF) - Korean government (MSIT) [2019R1C1C1003473]en
dc.description.versionPublished versionen
dc.format.mimetypeapplication/pdfen
dc.identifier.doihttps://doi.org/10.1112/S0010437X21007028en
dc.identifier.eissn1570-5846en
dc.identifier.issn0010-437Xen
dc.identifier.issue5en
dc.identifier.urihttp://hdl.handle.net/10919/104443en
dc.identifier.volume157en
dc.language.isoenen
dc.rightsCreative Commons Attribution 4.0 Internationalen
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/en
dc.titleBack stable Schubert calculusen
dc.title.serialCompositio Mathematicaen
dc.typeArticle - Refereeden
dc.type.dcmitypeTexten
dc.type.dcmitypeStillImageen

Files

Original bundle
Now showing 1 - 1 of 1
Thumbnail Image
Name:
back-stable-schubert-calculus.pdf
Size:
1.5 MB
Format:
Adobe Portable Document Format
Description:
Published version
Download

Collections

Scholarly Works, Mathematics