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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| Format: | Article |
| Language: | English |
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National Academy of Science of Ukraine
2007-05-01
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| Series: | Symmetry, Integrability and Geometry: Methods and Applications |
| Subjects: | |
| Online Access: | http://www.emis.de/journals/SIGMA/2007/072/ |
| _version_ | 1811193967339896832 |
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| author | Anatol N. Kirillov |
| author_facet | Anatol N. Kirillov |
| author_sort | Anatol N. Kirillov |
| collection | DOAJ |
| 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. |
| first_indexed | 2024-04-12T00:18:20Z |
| format | Article |
| id | doaj.art-c483ed84d70f429bb4d0bc8fbfc615d6 |
| institution | Directory Open Access Journal |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2024-04-12T00:18:20Z |
| publishDate | 2007-05-01 |
| publisher | National Academy of Science of Ukraine |
| record_format | Article |
| series | Symmetry, Integrability and Geometry: Methods and Applications |
| spelling | doaj.art-c483ed84d70f429bb4d0bc8fbfc615d62022-12-22T03:55:47ZengNational Academy of Science of UkraineSymmetry, Integrability and Geometry: Methods and Applications1815-06592007-05-013072Skew Divided Difference Operators and Schubert PolynomialsAnatol N. KirillovWe 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.http://www.emis.de/journals/SIGMA/2007/072/divided differencesnilCoxeter algebrasSchubert polynomials |
| spellingShingle | Anatol N. Kirillov Skew Divided Difference Operators and Schubert Polynomials Symmetry, Integrability and Geometry: Methods and Applications divided differences nilCoxeter algebras Schubert polynomials |
| 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 |
| topic | divided differences nilCoxeter algebras Schubert polynomials |
| url | http://www.emis.de/journals/SIGMA/2007/072/ |
| work_keys_str_mv | AT anatolnkirillov skewdivideddifferenceoperatorsandschubertpolynomials |