Representations of Hecke-Clifford superalgebras at roots of unity
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866917484266782720 |
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| author | Chen, Minjia Wan, Jinkui |
| author_facet | Chen, Minjia Wan, Jinkui |
| contents | In this article, we give a classification of irreducible completely splittable representations of affine Hecke-Clifford superalgebras $H_n^{\mathrm{aff}}(q)$ when $q^2$ is a primitive $h$-th root of unity. As an application, we derive a necessary and sufficient condition for the finite Hecke-Clifford superalgebra $H_n(q)$ to be semisimple. Specially we show that $H_n(q)$ is semisimple if and only $h >n$ in the case $h$ is odd and $h >2n$ in the case $h$ is even. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_11778 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Representations of Hecke-Clifford superalgebras at roots of unity Chen, Minjia Wan, Jinkui Representation Theory Combinatorics 20C08, 05E10, 17B10 In this article, we give a classification of irreducible completely splittable representations of affine Hecke-Clifford superalgebras $H_n^{\mathrm{aff}}(q)$ when $q^2$ is a primitive $h$-th root of unity. As an application, we derive a necessary and sufficient condition for the finite Hecke-Clifford superalgebra $H_n(q)$ to be semisimple. Specially we show that $H_n(q)$ is semisimple if and only $h >n$ in the case $h$ is odd and $h >2n$ in the case $h$ is even. |
| title | Representations of Hecke-Clifford superalgebras at roots of unity |
| topic | Representation Theory Combinatorics 20C08, 05E10, 17B10 |
| url | https://arxiv.org/abs/2605.11778 |