Notes on Schubert, Grothendieck and Key Polynomials

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Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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Symmetry, Integrability and Geometry: Methods and Applications, 2016, том 12
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dc.contributor.author	Kirillov, A.N.
dc.date.accessioned	2019-02-15T18:44:31Z
dc.date.available	2019-02-15T18:44:31Z
dc.date.issued	2016
dc.identifier.citation	Notes on Schubert, Grothendieck and Key Polynomials / A.N. Kirillov // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 72 назв. — англ.	uk_UA
dc.identifier.issn	1815-0659
dc.identifier.other	2010 Mathematics Subject Classification: 05E05; 05E10; 05A19
dc.identifier.other	DOI:10.3842/SIGMA.2016.034
dc.identifier.uri	http://dspace.nbuv.gov.ua/handle/123456789/147725
dc.description.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.	uk_UA
dc.description.sponsorship	A bit of history. Originally these notes have been designed as a continuation of [17]. The main purpose was to extend the methods developed in [18] to obtain by the use of plactic algebra, a noncommutative generating function for the key (or Demazure) polynomials introduced by A. Lascoux and M.-P. Sch¨utzenberger [53]. The results concerning the polynomials introduced in Section 4, except the Hecke–Grothendieck polynomials, see Definition 4.6, has been presented in my lecture-courses “Schubert Calculus” and have been delivered at the Graduate School of Mathematical Sciences, the University of Tokyo, November 1995 – April 1996, and at the Graduate School of Mathematics, Nagoya University, October 1998 – April 1999. I want to thank Professor M. Noumi and Professor T. Nakanishi who made these courses possible. Some early versions of the present notes are circulated around the world and now I was asked to put it for the wide audience. I would like to thank Professor M. Ishikawa (Department of Mathematics, Faculty of Education, University of the Ryukyus, Okinawa, Japan) and Professor S. Okada (Graduate School of Mathematics, Nagoya University, Nagoya, Japan) for valuable comments. My special thanks to the referees for very careful reading of a preliminary version of the present paper and many valuable remarks, comments and suggestions.	uk_UA
dc.language.iso	en	uk_UA
dc.publisher	Інститут математики НАН України	uk_UA
dc.relation.ispartof	Symmetry, Integrability and Geometry: Methods and Applications
dc.title	Notes on Schubert, Grothendieck and Key Polynomials	uk_UA
dc.type	Article	uk_UA
dc.status	published earlier	uk_UA