A quantum Murnaghan--Nakayama rule for the flag manifold
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866911130688946176 |
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| author | Benedetti, Carolina Bergeron, Nantel Colmenarejo, Laura Saliola, Franco Sottile, Frank |
| author_facet | Benedetti, Carolina Bergeron, Nantel Colmenarejo, Laura Saliola, Franco Sottile, Frank |
| contents | In this paper, we give a rule for the multiplication of a Schubert class by a tautological
class in the (small) quantum cohomology ring of the flag manifold.
As an intermediate step, we establish a formula for the multiplication of
a Schubert class by a quantum Schur polynomial indexed by a hook partition.
This entails a detailed analysis of chains and intervals in the
quantum Bruhat order.
This analysis allows us to use results of Leung--Li and of Postnikov to reduce quantum
products by hook Schur polynomials to the (known) classical product. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_05311 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A quantum Murnaghan--Nakayama rule for the flag manifold Benedetti, Carolina Bergeron, Nantel Colmenarejo, Laura Saliola, Franco Sottile, Frank Combinatorics Algebraic Geometry Quantum Algebra 05E05, 14N15 In this paper, we give a rule for the multiplication of a Schubert class by a tautological class in the (small) quantum cohomology ring of the flag manifold. As an intermediate step, we establish a formula for the multiplication of a Schubert class by a quantum Schur polynomial indexed by a hook partition. This entails a detailed analysis of chains and intervals in the quantum Bruhat order. This analysis allows us to use results of Leung--Li and of Postnikov to reduce quantum products by hook Schur polynomials to the (known) classical product. |
| title | A quantum Murnaghan--Nakayama rule for the flag manifold |
| topic | Combinatorics Algebraic Geometry Quantum Algebra 05E05, 14N15 |
| url | https://arxiv.org/abs/2406.05311 |