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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)
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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, $\beta$-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
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\paper Notes on Schubert, Grothendieck and Key Polynomials
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    • This publication is cited in the following 15 articles:
    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
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