Equivariant quasisymmetry and noncrossing partitions
Fuente:
arXiv
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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Soggetti: | |
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| _version_ | 1866909586623037440 |
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| author | Bergeron, Nantel Gagnon, Lucas Nadeau, Philippe Spink, Hunter Tewari, Vasu |
| author_facet | Bergeron, Nantel Gagnon, Lucas Nadeau, Philippe Spink, Hunter Tewari, Vasu |
| contents | We introduce a definition of ``equivariant quasisymmetry'' for polynomials in two sets of variables. Using this definition we define quasisymmetric generalizations of the theory of double Schur and double Schubert polynomials that we call double fundamental polynomials and double forest polynomials, where the subset of ``noncrossing partitions'' plays the role of $S_n$. In subsequent work we will show this combinatorics is governed by a new geometric construction we call the ``quasisymmetric flag variety'' which plays the same role for equivariant quasisymmetry as the usual flag variety plays in the classical story. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_15234 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Equivariant quasisymmetry and noncrossing partitions Bergeron, Nantel Gagnon, Lucas Nadeau, Philippe Spink, Hunter Tewari, Vasu Combinatorics Algebraic Geometry We introduce a definition of ``equivariant quasisymmetry'' for polynomials in two sets of variables. Using this definition we define quasisymmetric generalizations of the theory of double Schur and double Schubert polynomials that we call double fundamental polynomials and double forest polynomials, where the subset of ``noncrossing partitions'' plays the role of $S_n$. In subsequent work we will show this combinatorics is governed by a new geometric construction we call the ``quasisymmetric flag variety'' which plays the same role for equivariant quasisymmetry as the usual flag variety plays in the classical story. |
| title | Equivariant quasisymmetry and noncrossing partitions |
| topic | Combinatorics Algebraic Geometry |
| url | https://arxiv.org/abs/2504.15234 |