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Skew Divided Difference Operators and Schubert Polynomials
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2007, том 3
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Skew Divided Difference Operators and Schubert Polynomials
Інший ID:
2000 Mathematics Subject Classification: 05E15; 05E05
Посилання:
Skew Divided Difference Operators and Schubert Polynomials / A.N. Kirillov // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 12 назв. — англ.
Підтримка:
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.
Дата:
2007
Переглядів:
454
Завантажень:
310
Анотація:
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.
