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

Эта публикация цитируется в 15 статьях

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

Аннотация: 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.

Ключевые слова: 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

Поступила: 26 марта 2015 г.; в окончательном варианте 28 февраля 2016 г.; опубликована 29 марта 2016 г.

Язык публикации: английский

DOI: 10.3842/SIGMA.2016.034