Anatol N. Kirillov, “Notes on Schubert, Grothendieck and Key Polynomials”, SIGMA, 2016, Volume 12,034, 56 pp.

This article is cited in 15 papers

Notes on Schubert, Grothendieck and Key Polynomials

Anatol N. Kirillov^abc

^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

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.

MSC: 05E05; 05E10; 05A19

Received: March 26, 2015; in final form February 28, 2016; Published online March 29, 2016

Language: English

DOI: 10.3842/SIGMA.2016.034