On the semisimplicity and Schur elements of (super)symmetric superalgebras
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866915983858335744 |
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| author | Shi, Lei |
| author_facet | Shi, Lei |
| contents | In this paper, we use Schur elements to derive semisimplicity criteria for (super)symmetric superalgebras. We obtain a closed formula for the Schur elements of cyclotomic Hecke-Clifford superalgebras $\mathcal{H}^{f}_{\mathbb{K}}$. As applications, we prove that two trace functions $\gimel_n$ and $t_{1,n}$ on the Hecke-Clifford superalgebra, which are defined in different ways, are proportional. We give a semisimplicity criterion for $\mathcal{H}^{f}_{\mathbb{K}}$ when it is (super)symmetric. We also derive semisimplicity criteria for cyclotomic quiver Hecke superalgebras of types $A^{(1)}_{e}$, $C^{(1)}_{e}$, $A^{(2)}_{2e}$ and $D^{(2)}_{e+1}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_04745 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the semisimplicity and Schur elements of (super)symmetric superalgebras Shi, Lei Representation Theory In this paper, we use Schur elements to derive semisimplicity criteria for (super)symmetric superalgebras. We obtain a closed formula for the Schur elements of cyclotomic Hecke-Clifford superalgebras $\mathcal{H}^{f}_{\mathbb{K}}$. As applications, we prove that two trace functions $\gimel_n$ and $t_{1,n}$ on the Hecke-Clifford superalgebra, which are defined in different ways, are proportional. We give a semisimplicity criterion for $\mathcal{H}^{f}_{\mathbb{K}}$ when it is (super)symmetric. We also derive semisimplicity criteria for cyclotomic quiver Hecke superalgebras of types $A^{(1)}_{e}$, $C^{(1)}_{e}$, $A^{(2)}_{2e}$ and $D^{(2)}_{e+1}$. |
| title | On the semisimplicity and Schur elements of (super)symmetric superalgebras |
| topic | Representation Theory |
| url | https://arxiv.org/abs/2605.04745 |