Notes on Schubert, Grothendieck and Key Polynomials
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...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2016 |
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| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2016
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/147725 |
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| Cite this: | Notes on Schubert, Grothendieck and Key Polynomials / A.N. Kirillov // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 72 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862611578577223680 |
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| author | Kirillov, A.N. |
| author_facet | Kirillov, A.N. |
| citation_txt | Notes on Schubert, Grothendieck and Key Polynomials / A.N. Kirillov // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 72 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | 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.
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| first_indexed | 2025-11-29T00:21:34Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-147725 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-11-29T00:21:34Z |
| publishDate | 2016 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Kirillov, A.N. 2019-02-15T18:44:31Z 2019-02-15T18:44:31Z 2016 Notes on Schubert, Grothendieck and Key Polynomials / A.N. Kirillov // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 72 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 05E05; 05E10; 05A19 DOI:10.3842/SIGMA.2016.034 https://nasplib.isofts.kiev.ua/handle/123456789/147725 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. 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. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Notes on Schubert, Grothendieck and Key Polynomials Article published earlier |
| spellingShingle | Notes on Schubert, Grothendieck and Key Polynomials Kirillov, A.N. |
| title | Notes on Schubert, Grothendieck and Key Polynomials |
| title_full | Notes on Schubert, Grothendieck and Key Polynomials |
| title_fullStr | Notes on Schubert, Grothendieck and Key Polynomials |
| title_full_unstemmed | Notes on Schubert, Grothendieck and Key Polynomials |
| title_short | Notes on Schubert, Grothendieck and Key Polynomials |
| title_sort | notes on schubert, grothendieck and key polynomials |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/147725 |
| work_keys_str_mv | AT kirillovan notesonschubertgrothendieckandkeypolynomials |