Structure constants for Chern classes of Schubert cells

A formula for the structure constants of the multiplication of Schubert classes is obtained in (Rebecca and Allen. arXiv preprint arXiv:1909.05283 , 2019). In this note, we prove analogous formulae for the Chern–Schwartz–MacPherson (CSM) classes and Segre–Schwartz–MacPherson (SSM) classes of Schuber...

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Bibliographic Details
Published in:Mathematische Zeitschrift 2021-06, Vol.298 (1-2), p.193-213
Main Author: Su, Changjian
Format: Article
Language:English
Subjects:
Flags
Mathematics
Mathematics and Statistics
Multiplication
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Summary:A formula for the structure constants of the multiplication of Schubert classes is obtained in (Rebecca and Allen. arXiv preprint arXiv:1909.05283 , 2019). In this note, we prove analogous formulae for the Chern–Schwartz–MacPherson (CSM) classes and Segre–Schwartz–MacPherson (SSM) classes of Schubert cells in the flag variety. By the equivalence between the CSM classes and the stable basis elements for the cotangent bundle of the flag variety, a formula for the structure constants for the latter is also deduced.
ISSN:0025-5874
1432-1823
DOI:10.1007/s00209-020-02595-5