On the generalized graded cellular bases for cyclotomic quiver Hecke-Clifford superalgebras
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866911579862204416 |
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| author | Li, Shuo Shi, Lei |
| author_facet | Li, Shuo Shi, Lei |
| contents | In this paper, we construct semisimple deformations for cyclotomic quiver Hecke-Clifford superalgebras of types $A^{(1)}_{s-1}$, $C^{(1)}_{s}$, $A^{(2)}_{2s}$, $D^{(2)}_{s}$. We derive a unified dimension formula for the bi-weight spaces for cyclotomic quiver Hecke-Clifford superalgebras of types $A^{(1)}_{s-1}$, $C^{(1)}_{s}$, $A^{(2)}_{2s}$, $D^{(2)}_{s}$. We introduce the notion of generalized graded cellular superalgebra. We prove a large class of cyclotomic quiver Hecke-Clifford superalgebras of types $A^{(1)}_{s-1}$, $C^{(1)}_{s}$, $A^{(2)}_{2s}$, $D^{(2)}_{s}$ is generalized graded cellular. By taking idempotent truncation, this recovers the known graded cellualr results for cyclotomic quiver Hecke algebras of types $A^{(1)}_{s-1}$, $C^{(1)}_{s}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_04058 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the generalized graded cellular bases for cyclotomic quiver Hecke-Clifford superalgebras Li, Shuo Shi, Lei Representation Theory 20C08, 16W55, 16G10 In this paper, we construct semisimple deformations for cyclotomic quiver Hecke-Clifford superalgebras of types $A^{(1)}_{s-1}$, $C^{(1)}_{s}$, $A^{(2)}_{2s}$, $D^{(2)}_{s}$. We derive a unified dimension formula for the bi-weight spaces for cyclotomic quiver Hecke-Clifford superalgebras of types $A^{(1)}_{s-1}$, $C^{(1)}_{s}$, $A^{(2)}_{2s}$, $D^{(2)}_{s}$. We introduce the notion of generalized graded cellular superalgebra. We prove a large class of cyclotomic quiver Hecke-Clifford superalgebras of types $A^{(1)}_{s-1}$, $C^{(1)}_{s}$, $A^{(2)}_{2s}$, $D^{(2)}_{s}$ is generalized graded cellular. By taking idempotent truncation, this recovers the known graded cellualr results for cyclotomic quiver Hecke algebras of types $A^{(1)}_{s-1}$, $C^{(1)}_{s}$. |
| title | On the generalized graded cellular bases for cyclotomic quiver Hecke-Clifford superalgebras |
| topic | Representation Theory 20C08, 16W55, 16G10 |
| url | https://arxiv.org/abs/2604.04058 |