On the irreducibility of singular braid group representations
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866914163891109888 |
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| author | Nasser, Mohamad N. |
| author_facet | Nasser, Mohamad N. |
| contents | In this article, we study the irreducibility of representations of the singular braid group on $n$ strands, namely $SB_n$. Our first finding is the determination of the forms of all irreducible representations $ρ: SB_2 \to GL_2(\mathbb{C})$. The second finding is the determination of the forms of all irreducible representations $ρ: SB_3 \to GL_2(\mathbb{C})$, together with the introduction of the forms of some irreducible representations $ρ: SB_3 \to GL_3(\mathbb{C})$. The third finding is the study of the irreducibility of the homogeneous local representations of $SB_n$ for all $n\geq 3$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2508_11580 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the irreducibility of singular braid group representations Nasser, Mohamad N. Representation Theory 20F36 In this article, we study the irreducibility of representations of the singular braid group on $n$ strands, namely $SB_n$. Our first finding is the determination of the forms of all irreducible representations $ρ: SB_2 \to GL_2(\mathbb{C})$. The second finding is the determination of the forms of all irreducible representations $ρ: SB_3 \to GL_2(\mathbb{C})$, together with the introduction of the forms of some irreducible representations $ρ: SB_3 \to GL_3(\mathbb{C})$. The third finding is the study of the irreducibility of the homogeneous local representations of $SB_n$ for all $n\geq 3$. |
| title | On the irreducibility of singular braid group representations |
| topic | Representation Theory 20F36 |
| url | https://arxiv.org/abs/2508.11580 |