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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2511.00980 |
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| _version_ | 1866908670597529600 |
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| author | Chen, Yiming Fan, Neil J. Y. Xiong, Rui Yao, Ming |
| author_facet | Chen, Yiming Fan, Neil J. Y. Xiong, Rui Yao, Ming |
| contents | In this paper, we establish a new geometric setting for bumpless pipe dreams and double Schubert polynomials. Building on the notion of bumpless pipe dream fragments, we define clan polynomials as their weight generating functions. It turns out that clan polynomials arise naturally in the equivariant geometry of ($GL_p\times GL_q$)-orbits over the flag variety $Fl_{p+q}$ parametrized by $(p,q)$-clans. Furthermore, we show that the coefficients in the equivariant Schubert expansion of the fundamental classes of ($GL_p\times GL_q$)-orbit closures are exactly clan polynomials, which resolves an open problem posed by Wyser and Yong. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_00980 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Bumpless Pipe Dream Fragments -- Equivariant Geometry of Clans Chen, Yiming Fan, Neil J. Y. Xiong, Rui Yao, Ming Combinatorics Algebraic Geometry In this paper, we establish a new geometric setting for bumpless pipe dreams and double Schubert polynomials. Building on the notion of bumpless pipe dream fragments, we define clan polynomials as their weight generating functions. It turns out that clan polynomials arise naturally in the equivariant geometry of ($GL_p\times GL_q$)-orbits over the flag variety $Fl_{p+q}$ parametrized by $(p,q)$-clans. Furthermore, we show that the coefficients in the equivariant Schubert expansion of the fundamental classes of ($GL_p\times GL_q$)-orbit closures are exactly clan polynomials, which resolves an open problem posed by Wyser and Yong. |
| title | Bumpless Pipe Dream Fragments -- Equivariant Geometry of Clans |
| topic | Combinatorics Algebraic Geometry |
| url | https://arxiv.org/abs/2511.00980 |