Symmetry, Integrability and Geometry: Methods and Applications
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS


SIGMA:
Year:
Volume:
Issue:
Page:
Find




Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register

Symmetry, Integrability and Geometry: Methods and Applications, 2016, Volume 12, 034, 56 pp.
DOI: https://doi.org/10.3842/SIGMA.2016.034 (Mi sigma1116) 		 
This article is cited in 15 scientific papers (total in 15 papers)

Notes on Schubert, Grothendieck and Key Polynomials

Anatol N. Kirillovabc

a Research Institute for Mathematical Sciences, Kyoto University
b Department of Mathematics, National Research University Higher School of Economics, 7 Vavilova Str., 117312, Moscow, Russia
c The Kavli Institute for the Physics and Mathematics of the Universe (IPMU), 5-1-5 Kashiwanoha, Kashiwa, 277-8583, Japan
Full-text PDF (816 kB) Citations (15)
References:
PDF
HTML
DOI: https://doi.org/10.3842/SIGMA.2016.034
Abstract: We introduce common generalization of (double) Schubert, Grothendieck, Demazure, dual and stable Grothendieck polynomials, and Di Francesco–Zinn-Justin polynomials. Our approach is based on the study of algebraic and combinatorial properties of the reduced rectangular plactic algebra and associated Cauchy kernels.
Keywords: plactic monoid and reduced plactic algebras; nilCoxeter and idCoxeter algebras; Schubert, β-Grothendieck, key and (double) key-Grothendieck, and Di Francesco–Zinn-Justin polynomials; Cauchy's type kernels and symmetric, totally symmetric plane partitions, and alternating sign matrices; noncrossing Dyck paths and (rectangular) Schubert polynomials; double affine nilCoxeter algebras.
Received: March 26, 2015; in final form February 28, 2016; Published online March 29, 2016
Bibliographic databases:
Document Type: Article
MSC: 05E05; 05E10; 05A19
Language: English
Citation: Anatol N. Kirillov, “Notes on Schubert, Grothendieck and Key Polynomials”, SIGMA, 12 (2016), 034, 56 pp.
Citation in format AMSBIB
\Bibitem{Kir16}
\by Anatol~N.~Kirillov
\paper Notes on Schubert, Grothendieck and Key Polynomials
\jour SIGMA
\yr 2016
\vol 12
\papernumber 034
\totalpages 56
\mathnet{http://mi.mathnet.ru/sigma1116}
\crossref{https://doi.org/10.3842/SIGMA.2016.034}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000374457600001}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84962090123}
Linking options:
  • https://www.mathnet.ru/eng/sigma1116
  • https://www.mathnet.ru/eng/sigma/v12/p34
    • This publication is cited in the following 15 articles:
    1. Mark Shimozono, Tianyi Yu, “Grothendieck-to-Lascoux expansions”, Trans. Amer. Math. Soc., 376:7 (2023), 5181  crossref
    2. Ben Brubaker, Claire Frechette, Andrew Hardt, Emily Tibor, Katherine Weber, “Frozen pipes: lattice models for Grothendieck polynomials”, Algebraic Combinatorics, 6:3 (2023), 789  crossref
    3. Zhang Z., Chen Yu., “A Weak Version of Kirillov'S Conjecture on Hecke-Grothendieck Polynomials”, J. Comb. Theory Ser. A, 186 (2022), 105555  crossref  mathscinet  isi
    4. Oliver Pechenik, Travis Scrimshaw, “K-theoretic crystals for set-valued tableaux of rectangular shapes”, Algebraic Combinatorics, 5:3 (2022), 515  crossref
    5. S. C. Billey, B. Rhoades, V. Tewari, “Boolean product polynomials, Schur positivity, and Chern plethysm”, Int. Math. Res. Notices, 2021:21 (2021), 16636–16670  crossref  mathscinet  isi  scopus
    6. K. Motegi, “Integrable models and k-theoretic pushforward of Grothendieck classes”, Nucl. Phys. B, 971 (2021), 115513  crossref  mathscinet  isi  scopus
    7. C. Monical, O. Pechenik, D. Searles, “Polynomials from combinatorial k-theory”, Can. J. Math.-J. Can. Math., 73:1 (2021), 29–62  crossref  mathscinet  isi
    8. CARA MONICAL, OLIVER PECHENIK, TRAVIS SCRIMSHAW, “CRYSTAL STRUCTURES FOR SYMMETRIC GROTHENDIECK POLYNOMIALS”, Transformation Groups, 26:3 (2021), 1025  crossref
    9. K. Motegi, “Integrability approach to Feher–Nemethi–Rimanyi–Guo–Sun type identities for factorial Grothendieck polynomials”, Nucl. Phys. B, 954 (2020), 114998  crossref  mathscinet  isi  scopus
    10. David Anderson, William Fulton, “Vexillary signed permutations revisited”, Algebraic Combinatorics, 3:5 (2020), 1041  crossref
    11. J. Blasiak, R. I. Liu, “Kronecker coefficients and noncommutative super Schur functions”, J. Comb. Theory Ser. A, 158 (2018), 315–361  crossref  mathscinet  zmath  isi
    12. J. Blasiak, S. Fomin, “Noncommutative Schur functions, switchboards, and Schur positivity”, Sel. Math.-New Ser., 23:1 (2017), 727–766  crossref  mathscinet  zmath  isi  scopus
    13. A. N. Kirillov, H. Naruse, “Construction of double Grothendieck polynomials of classical types using idCoxeter algebras”, Tokyo J. Math., 39:3 (2017), 695–728  crossref  mathscinet  zmath  isi
    14. K. Motegi, “Dual wavefunction of the symplectic ice”, Rep. Math. Phys., 80:3 (2017), 391–414  crossref  mathscinet  zmath  isi
    15. K. Motegi, “Combinatorial properties of symmetric polynomials from integrable vertex models in finite lattice”, J. Math. Phys., 58:9 (2017), 091703  crossref  mathscinet  zmath  isi
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Symmetry, Integrability and Geometry: Methods and Applications
    Statistics & downloads:
    Abstract page:232
    Full-text PDF :261
    References:54
     
      Contact us:
    		  Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2025