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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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2007 |
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| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2007
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| Online Access: | https://nasplib.isofts.kiev.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| _version_ | 1862647115314888704 |
|---|---|
| author | Kirillov, A.N. |
| author_facet | Kirillov, A.N. |
| 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. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| 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.
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| first_indexed | 2025-12-01T12:02:57Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-147361 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-01T12:02:57Z |
| publishDate | 2007 |
| publisher | Інститут математики НАН України |
| 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 |
| spellingShingle | Skew Divided Difference Operators and Schubert Polynomials Kirillov, A.N. |
| title | 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_short | Skew Divided Difference Operators and Schubert Polynomials |
| title_sort | skew divided difference operators and schubert polynomials |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/147361 |
| work_keys_str_mv | AT kirillovan skewdivideddifferenceoperatorsandschubertpolynomials |