The superspace coinvariant ring of type B
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866908384897269760 |
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| author | Bhattacharya, Sutanay |
| author_facet | Bhattacharya, Sutanay |
| contents | Given the rank $n$ superspace $Ω_n$, the ring of polynomial-valued differential forms on $\mathbb C^n$, one can define an action of hyperoctahedral group $\mathfrak B_n$ on it. This leads to a superspace coinvariant ideal $SR_n^B$, defined as the quotient of $Ω_n$ by two-sided ideal generated by all $\mathfrak B_n$ invariants with vanishing constant terms. We derive the Hilbert series of $SR^B_n$ conjectured by Sagan and Swanson, and prove an operator theorem that yields a concrete description of the superharmonic space $SH^B_n$ associated to $SR^B_n$ as conjectured by Swanson and Wallach. We also derive an explicit basis of $SR^B_n$ using the theory of hyperplane arrangements. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_24122 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The superspace coinvariant ring of type B Bhattacharya, Sutanay Combinatorics Commutative Algebra Representation Theory 05E10 Given the rank $n$ superspace $Ω_n$, the ring of polynomial-valued differential forms on $\mathbb C^n$, one can define an action of hyperoctahedral group $\mathfrak B_n$ on it. This leads to a superspace coinvariant ideal $SR_n^B$, defined as the quotient of $Ω_n$ by two-sided ideal generated by all $\mathfrak B_n$ invariants with vanishing constant terms. We derive the Hilbert series of $SR^B_n$ conjectured by Sagan and Swanson, and prove an operator theorem that yields a concrete description of the superharmonic space $SH^B_n$ associated to $SR^B_n$ as conjectured by Swanson and Wallach. We also derive an explicit basis of $SR^B_n$ using the theory of hyperplane arrangements. |
| title | The superspace coinvariant ring of type B |
| topic | Combinatorics Commutative Algebra Representation Theory 05E10 |
| url | https://arxiv.org/abs/2505.24122 |