On (super)symmetrizing forms and Schur elements of cyclotomic Hecke-Clifford algebras
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866912987159199744 |
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| author | Li, Shuo Shi, Lei |
| author_facet | Li, Shuo Shi, Lei |
| contents | In this paper, we introduce Schur elements for supersymmetrizing superalgebras. We show that the cyclotomic Hecke-Clifford algebra $\mathcal{H}^f_{c}(n)$ is supersymmetric if $f=f^{(\mathtt{0})}_{\underline{Q}}$ and, symmetric if $f=f^{(\mathtt{s})}_{\underline{Q}}$ and an invertibility condition holds. In the semisimple case, we compute the Schur elements for both $\mathcal{H}^f_{c}(n)$ and the cyclotomic Sergeev algebra $\mathcal{h}^g_{c}(n)$. As applications, we define new symmetrizing forms on the Hecke-Clifford algebra $\mathcal{H}(n)$ and on the cyclotomic quiver Hecke algebras of types $A^{(1)}_{e-1}$ and $C^{(1)}_e$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_18395 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On (super)symmetrizing forms and Schur elements of cyclotomic Hecke-Clifford algebras Li, Shuo Shi, Lei Representation Theory 20C08, 16W55, 16G99 In this paper, we introduce Schur elements for supersymmetrizing superalgebras. We show that the cyclotomic Hecke-Clifford algebra $\mathcal{H}^f_{c}(n)$ is supersymmetric if $f=f^{(\mathtt{0})}_{\underline{Q}}$ and, symmetric if $f=f^{(\mathtt{s})}_{\underline{Q}}$ and an invertibility condition holds. In the semisimple case, we compute the Schur elements for both $\mathcal{H}^f_{c}(n)$ and the cyclotomic Sergeev algebra $\mathcal{h}^g_{c}(n)$. As applications, we define new symmetrizing forms on the Hecke-Clifford algebra $\mathcal{H}(n)$ and on the cyclotomic quiver Hecke algebras of types $A^{(1)}_{e-1}$ and $C^{(1)}_e$. |
| title | On (super)symmetrizing forms and Schur elements of cyclotomic Hecke-Clifford algebras |
| topic | Representation Theory 20C08, 16W55, 16G99 |
| url | https://arxiv.org/abs/2511.18395 |