Geodesic
Infinite flags and Schubert polynomials
Forum of Mathematics, Sigma, Tome 13 (2025) no. 1, p. e36

Voir la notice de l'article provenant de la source Cambridge University Press

We study Schubert polynomials using geometry of infinite-dimensional flag varieties and degeneracy loci. Applications include Graham-positivity of coefficients appearing in equivariant coproduct formulas and expansions of back-stable and enriched Schubert polynomials. We also construct an embedding of the type C flag variety and study the corresponding pullback map on (equivariant) cohomology rings. 
Anderson, David. Infinite flags and Schubert polynomials. Forum of Mathematics, Sigma, Tome 13 (2025) no. 1, p. e36. doi: 10.1017/fms.2024.99
@article{10_1017_fms_2024_99,
     author = {Anderson, David},
     title = {Infinite flags and {Schubert} polynomials},
     journal = {Forum of Mathematics, Sigma},
     pages = {e36},
     year = {2025},
     volume = {13},
     number = {1},
     doi = {10.1017/fms.2024.99},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/fms.2024.99/}
}
TY  - JOUR
AU  - Anderson, David
TI  - Infinite flags and Schubert polynomials
JO  - Forum of Mathematics, Sigma
PY  - 2025
SP  - e36
VL  - 13
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.1017/fms.2024.99/
DO  - 10.1017/fms.2024.99
ID  - 10_1017_fms_2024_99
ER  - 
%0 Journal Article
%A Anderson, David
%T Infinite flags and Schubert polynomials
%J Forum of Mathematics, Sigma
%D 2025
%P e36
%V 13
%N 1
%U http://geodesic.mathdoc.fr/articles/10.1017/fms.2024.99/
%R 10.1017/fms.2024.99
%F 10_1017_fms_2024_99

[1] Anderson, D., ‘Strong equivariant positivity for homogeneous varieties and back-stable coproduct coefficients’, Preprint, 2023, . Google Scholar | arXiv

[2] Anderson, D., ‘Integral equivariant cohomology of affine Grassmannians’, Canad. Math. Bull., to appear (2023). Google Scholar | DOI

[3] Anderson, D. and Fulton, W., ‘Degeneracy loci, Pfaffians, and vexillary signed permutations in Types B, C, and D’, Preprint, 2012, . Google Scholar | arXiv

[4] Anderson, D. and Fulton, W., ‘Chern class formulas for classical-type degeneracy loci’, Compos. Math. 154 (2018), 1746–1774. Google Scholar | DOI

[5] Anderson, D. and Fulton, W., ‘Schubert polynomials in type A and C’, Preprint, 2021, . Google Scholar | arXiv

[6] Anderson, D. and Fulton, W., Equivariant Cohomology in Algebraic Geometry (Cambridge University Press, Cambridge, 2023). Google Scholar | DOI

[7] Bergeron, N. and Sottile, F., ‘Schubert polynomials, the Bruhat order, and the geometry of flag manifolds’, Duke Math. J. 95(2) (1998), 373–423. Google Scholar | DOI

[8] Billey, S. and Haiman, M., ‘Schubert polynomials for the classical group,’ J. Amer. Math. Soc. 8 (1995), 443–482. Google Scholar | DOI

[9] Buch, A., ‘A Littlewood-Richardson rule for the K-theory of Grassmannians’, Acta Math. 189(1) (2002), 37–78. Google Scholar | DOI

[10] Buch, A. and Fulton, W., ‘Chern class formulas for quiver varieties’, Invent. Math. 135(3) (1999), 665–687. Google Scholar | DOI

[11] Buch, A. and Rimányi, R., ‘Specializations of Grothendieck polynomials’, C. R. Acad. Sci. Paris, Ser. I 339 (2004), 1–4. Google Scholar | DOI

[12] Fomin, S. and Kirillov, A. N., ‘Combinatorial B n -analogues of Schubert polynomials’, Trans. Amer. Math. Soc. 348(9) (1996), 3591–3620. Google Scholar | DOI

[13] Fulton, W., Intersection Theory (Springer-Verlag, 1984; second edn., 1998). Google Scholar | DOI

[14] Fulton, W., ‘Flags, Schubert polynomials, degeneracy loci, and determinantal formulas’, Duke Math. J. 65 (1992), 381–420. Google Scholar | DOI

[15] Graham, W., ‘Positivity in equivariant Schubert calculus’, Duke Math. J. 109 (2001), 599–614. Google Scholar | DOI

[16] Ikeda, T., Naruse, H. and Mihalcea, L., ‘Double Schubert polynomials for the classical groups’, Adv. Math. 226 (2011), 840–886. Google Scholar | DOI

[17] Kashiwara, M., ‘The flag manifold of Kac-Moody Lie algebra’, in Algebraic Analysis, Geometry, and Number Theory (Baltimore, MD, 1988) (Johns Hopkins Univ. Press, Baltimore, MD, 1989), 161–190. Google Scholar

[18] Kempf, G. and Laksov, D., ‘The determinantal formula of Schubert calculus’, Acta Math. 132 (1974), 153–162. Google Scholar | DOI

[19] Knutson, A., Lam, T. and Speyer, D., ‘Positroid varieties: juggling and geometry’, Compos. Math. 149(10) (2013), 1710–1752. Google Scholar | DOI

[20] Knutson, A. and Lederer, M., ‘A K -deformation of the ring of symmetric functions’, Preprint, 2015, . Google Scholar | arXiv | DOI

[21] Lam, T., Lee, S. and Shimozono, M., ‘Back stable Schubert calculus’, Compos. Math. 157 (2021), 883–962. Google Scholar | DOI

[22] Lascoux, A. and Schützenberger, M.-P., ‘Polynômes de Schubert’, C. R. Acad. Sci. Paris Sér. I Math. 294 (1982), 447–450. Google Scholar

[23] Macdonald, I. G., Symmetric Functions and Hall Polynomials, second edn., (Oxford University Press, 1995). Google Scholar | DOI

[24] Molev, A. I., ‘Comultiplication rules for the double Schur functions and Cauchy identities’, Electron. J. Combin. 16 (2009), #R13. Google Scholar | DOI

[25] Pressley, A. and Segal, G., Loop Groups (Oxford, 1986). Google Scholar

[26] Stembridge, J. R., ‘Shifted tableaux and the projective representations of symmetric groups’, Adv. Math. 74(1) (1989), 87–134. Google Scholar | DOI

[27] Thomas, H. and Yong, A., ‘The direct sum map on Grassmannians and jeu de taquin for increasing tableaux’, Int. Math. Res. Not. IMRN 12 (2011), 2766–2793. Google Scholar

Cité par Sources :