Skew Divided Difference Operators and Schubert Polynomials

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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Date:2007
Main Author: Kirillov, A.N.
Format: Article
Language:English
Published: Інститут математики НАН України 2007
Series:Symmetry, Integrability and Geometry: Methods and Applications
Online Access:http://dspace.nbuv.gov.ua/handle/123456789/147361
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Journal Title:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Cite this:Skew Divided Difference Operators and Schubert Polynomials / A.N. Kirillov // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 12 назв. — англ.

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
id irk-123456789-147361
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spelling irk-123456789-1473612019-02-15T01:23:01Z Skew Divided Difference Operators and Schubert Polynomials Kirillov, A.N. 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. 2007 Article 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 http://dspace.nbuv.gov.ua/handle/123456789/147361 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
language English
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.
format Article
author Kirillov, A.N.
spellingShingle Kirillov, A.N.
Skew Divided Difference Operators and Schubert Polynomials
Symmetry, Integrability and Geometry: Methods and Applications
author_facet Kirillov, A.N.
author_sort Kirillov, A.N.
title Skew Divided Difference Operators and Schubert Polynomials
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
publisher Інститут математики НАН України
publishDate 2007
url http://dspace.nbuv.gov.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.
series Symmetry, Integrability and Geometry: Methods and Applications
work_keys_str_mv AT kirillovan skewdivideddifferenceoperatorsandschubertpolynomials
first_indexed 2025-07-11T01:54:53Z
last_indexed 2025-07-11T01:54:53Z
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