Skew Divided Difference Operators and Schubert Polynomials

We study an action of the skew divided difference operators on the Schubert polynomials and give an explicit formula for structural constants for the Schubert polynomials in terms of certain weighted paths in the Bruhat order on the symmetric group. We also prove that, under certain assumptions, the...

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Опубліковано в: :Symmetry, Integrability and Geometry: Methods and Applications
Дата:2007
Автор: Kirillov, A.N.
Формат: Стаття
Мова:English
Опубліковано: Інститут математики НАН України 2007
Онлайн доступ:https://nasplib.isofts.kiev.ua/handle/123456789/147361
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Назва журналу:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Цитувати:Skew Divided Difference Operators and Schubert Polynomials / A.N. Kirillov // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 12 назв. — англ.

Репозитарії

Digital Library of Periodicals of National Academy of Sciences of Ukraine
id nasplib_isofts_kiev_ua-123456789-147361
record_format dspace
spelling Kirillov, A.N.
2019-02-14T14:43:14Z
2019-02-14T14:43:14Z
2007
Skew Divided Difference Operators and Schubert Polynomials / A.N. Kirillov // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 12 назв. — англ.
1815-0659
2000 Mathematics Subject Classification: 05E15; 05E05
https://nasplib.isofts.kiev.ua/handle/123456789/147361
We study an action of the skew divided difference operators on the Schubert polynomials and give an explicit formula for structural constants for the Schubert polynomials in terms of certain weighted paths in the Bruhat order on the symmetric group. We also prove that, under certain assumptions, the skew divided difference operators transform the Schubert polynomials into polynomials with positive integer coefficients.
This paper is a contribution to the Vadim Kuznetsov Memorial Issue ‘Integrable Systems and Related Topics’. This note is based on the lectures “Schubert polynomials” delivered in the Spring 1995 at the University of Minneapolis and in the Spring 1996 at the University of Tokyo. I would like to thank my colleagues from these universities for hospitality and support.The first version of this paper has appeared as a preprint q-alg/9712053.
en
Інститут математики НАН України
Symmetry, Integrability and Geometry: Methods and Applications
Skew Divided Difference Operators and Schubert Polynomials
Article
published earlier
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
title Skew Divided Difference Operators and Schubert Polynomials
spellingShingle Skew Divided Difference Operators and Schubert Polynomials
Kirillov, A.N.
title_short Skew Divided Difference Operators and Schubert Polynomials
title_full Skew Divided Difference Operators and Schubert Polynomials
title_fullStr Skew Divided Difference Operators and Schubert Polynomials
title_full_unstemmed Skew Divided Difference Operators and Schubert Polynomials
title_sort skew divided difference operators and schubert polynomials
author Kirillov, A.N.
author_facet Kirillov, A.N.
publishDate 2007
language English
container_title Symmetry, Integrability and Geometry: Methods and Applications
publisher Інститут математики НАН України
format Article
description We study an action of the skew divided difference operators on the Schubert polynomials and give an explicit formula for structural constants for the Schubert polynomials in terms of certain weighted paths in the Bruhat order on the symmetric group. We also prove that, under certain assumptions, the skew divided difference operators transform the Schubert polynomials into polynomials with positive integer coefficients.
issn 1815-0659
url https://nasplib.isofts.kiev.ua/handle/123456789/147361
citation_txt Skew Divided Difference Operators and Schubert Polynomials / A.N. Kirillov // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 12 назв. — англ.
work_keys_str_mv AT kirillovan skewdivideddifferenceoperatorsandschubertpolynomials
first_indexed 2025-12-01T12:02:57Z
last_indexed 2025-12-01T12:02:57Z
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