Coordinate rings of regular semisimple Hessenberg varieties and cohomology rings of regular nilpotent Hessenberg varieties
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866911316025802752 |
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| author | Horiguchi, Tatsuya |
| author_facet | Horiguchi, Tatsuya |
| contents | The polynomials $f_{i,j}$ are introduced by Abe-Harada-Horiguchi-Masuda to produce an explicit presentation by generators and relations of the cohomology rings of regular nilpotent Hessenberg varieties. In this paper we quantize the polynomials $f_{i,j}$ by a method of Fomin-Gelfand-Postnikov. Our main result states that their quantizations $F_{i,j}$ are related to the coordinate rings of regular semisimple Hessenberg varieties. This result yields a connection between the coordinate rings of regular semisimple Hessenberg varieties and the cohomology rings of regular nilpotent Hessenberg varieties. We also provide the quantized recursive formula for $F_{i,j}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_11565 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Coordinate rings of regular semisimple Hessenberg varieties and cohomology rings of regular nilpotent Hessenberg varieties Horiguchi, Tatsuya Algebraic Geometry Combinatorics 14M15, 05E05, 14N35 The polynomials $f_{i,j}$ are introduced by Abe-Harada-Horiguchi-Masuda to produce an explicit presentation by generators and relations of the cohomology rings of regular nilpotent Hessenberg varieties. In this paper we quantize the polynomials $f_{i,j}$ by a method of Fomin-Gelfand-Postnikov. Our main result states that their quantizations $F_{i,j}$ are related to the coordinate rings of regular semisimple Hessenberg varieties. This result yields a connection between the coordinate rings of regular semisimple Hessenberg varieties and the cohomology rings of regular nilpotent Hessenberg varieties. We also provide the quantized recursive formula for $F_{i,j}$. |
| title | Coordinate rings of regular semisimple Hessenberg varieties and cohomology rings of regular nilpotent Hessenberg varieties |
| topic | Algebraic Geometry Combinatorics 14M15, 05E05, 14N35 |
| url | https://arxiv.org/abs/2512.11565 |