Diagonal Supersymmetry for Coinvariant Rings
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866908372873248768 |
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| author | Lentfer, John |
| author_facet | Lentfer, John |
| contents | For finite groups $G$, we show that bosonic-fermionic coinvariant rings have a natural $U(\mathfrak{gl}(k|j)) \otimes \mathbb{C}[G]$-module structure. In particular, we show that their character series are a sum of super Schur functions $s_λ(\mathbf{q}/\mathbf{u})$ times irreducible characters of $G$ with universal coefficients, which do not depend on $k,j$. In the case where $G$ is the symmetric group with diagonal action, this proves the "Diagonal Supersymmetry" conjecture of Bergeron (2020). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_14885 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Diagonal Supersymmetry for Coinvariant Rings Lentfer, John Combinatorics Representation Theory 05E05 (Primary) 05E10, 20C30, 17B10 (Secondary) For finite groups $G$, we show that bosonic-fermionic coinvariant rings have a natural $U(\mathfrak{gl}(k|j)) \otimes \mathbb{C}[G]$-module structure. In particular, we show that their character series are a sum of super Schur functions $s_λ(\mathbf{q}/\mathbf{u})$ times irreducible characters of $G$ with universal coefficients, which do not depend on $k,j$. In the case where $G$ is the symmetric group with diagonal action, this proves the "Diagonal Supersymmetry" conjecture of Bergeron (2020). |
| title | Diagonal Supersymmetry for Coinvariant Rings |
| topic | Combinatorics Representation Theory 05E05 (Primary) 05E10, 20C30, 17B10 (Secondary) |
| url | https://arxiv.org/abs/2505.14885 |