TY - JOUR
T1 - The Prism tableau model for Schubert polynomials
AU - Weigandt, Anna
AU - Yong, Alexander
N1 - Funding Information:
We thank Laura Escobar, Sergey Fomin, Allen Knutson, Victor Reiner, Steven Sam, Mark Shimozono for helpful remarks. We also thank the anonymous referees for their comments and suggestions. We made extensive use of Macaulay2 during our investigation. AW and AY were supported by a UIUC Campus Research Board RB15060 and by NSF DMS grant 1500691 .
Publisher Copyright:
© 2017 Elsevier Inc.
PY - 2018/2
Y1 - 2018/2
N2 - The Schubert polynomials lift the Schur basis of symmetric polynomials into a basis for Z[x1,x2,…]. We suggest the prism tableau model for these polynomials. A novel aspect of this alternative to earlier results is that it directly invokes semistandard tableaux; it does so as part of a colored tableau amalgam. In the Grassmannian case, a prism tableau with colors ignored is a semistandard Young tableau. Our arguments are developed from the Gröbner geometry of matrix Schubert varieties.
AB - The Schubert polynomials lift the Schur basis of symmetric polynomials into a basis for Z[x1,x2,…]. We suggest the prism tableau model for these polynomials. A novel aspect of this alternative to earlier results is that it directly invokes semistandard tableaux; it does so as part of a colored tableau amalgam. In the Grassmannian case, a prism tableau with colors ignored is a semistandard Young tableau. Our arguments are developed from the Gröbner geometry of matrix Schubert varieties.
KW - BiGrassmannian permutations
KW - Schubert polynomials
KW - Semistandard tableaux
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U2 - 10.1016/j.jcta.2017.09.009
DO - 10.1016/j.jcta.2017.09.009
M3 - Article
AN - SCOPUS:85033443583
VL - 154
SP - 551
EP - 582
JO - Journal of Combinatorial Theory - Series A
JF - Journal of Combinatorial Theory - Series A
SN - 0097-3165
ER -