Two-row Delta Springer varieties
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866914016465518592 |
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| author | Lacabanne, Abel Vaz, Pedro Wilbert, Arik |
| author_facet | Lacabanne, Abel Vaz, Pedro Wilbert, Arik |
| contents | We study the geometry and topology of $Δ$-Springer varieties associated with two-row partitions. These varieties were introduced in recent work by Griffin-Levinson-Woo to give a geometric realization of a symmetric function appearing in the Delta conjecture by Haglund-Remmel-Wilson. We provide an explicit and combinatorial description of the irreducible components of the two-row $Δ$-Springer variety and compare it to the ordinary two-row Springer fiber as well as Kato's exotic Springer fiber corresponding to a one-row bipartition. In addition to that, we extend the action of the symmetric group on the homology of the two-row $Δ$-Springer variety to an action of a degenerate affine Hecke algebra and relate this action to a $\mathfrak{gl}_{2}$-tensor space. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_10792 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Two-row Delta Springer varieties Lacabanne, Abel Vaz, Pedro Wilbert, Arik Representation Theory Combinatorics Quantum Algebra Primary: 14M15, Secondary: 05E10, 20C08 We study the geometry and topology of $Δ$-Springer varieties associated with two-row partitions. These varieties were introduced in recent work by Griffin-Levinson-Woo to give a geometric realization of a symmetric function appearing in the Delta conjecture by Haglund-Remmel-Wilson. We provide an explicit and combinatorial description of the irreducible components of the two-row $Δ$-Springer variety and compare it to the ordinary two-row Springer fiber as well as Kato's exotic Springer fiber corresponding to a one-row bipartition. In addition to that, we extend the action of the symmetric group on the homology of the two-row $Δ$-Springer variety to an action of a degenerate affine Hecke algebra and relate this action to a $\mathfrak{gl}_{2}$-tensor space. |
| title | Two-row Delta Springer varieties |
| topic | Representation Theory Combinatorics Quantum Algebra Primary: 14M15, Secondary: 05E10, 20C08 |
| url | https://arxiv.org/abs/2407.10792 |