Dual partially harmonic tensors and quantized Schur--Weyl duality
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866912911347154944 |
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| author | Wang, Pei Xiao, Zhankui |
| author_facet | Wang, Pei Xiao, Zhankui |
| contents | Let $V$ be a $2m$-dimensional symplectic space over an infinite field $K$. Let $\mathfrak{B}^{(f)}_{n,K}$ be the two-sided ideal of the Birman--Murakami--Wenzl algebra $\mathfrak{B}_{n,K}$ generated by $E_1E_3\cdots E_{2f-1}$ with $1\leq f\leq\left\lfloor \frac n2 \right\rfloor$. In this paper, using the diagram category of framed tangles and canonical basis, we prove that the natural homomorphism from $\mathfrak{B}_{n,K}/\mathfrak{B}^{(f)}_{n,K}$ to $ \mathrm{End}_{U_q(\mathfrak{sp}_{2m})}\left(V^{\otimes n}/\left(V^{\otimes n}\cdot \mathfrak{B}^{(f)}_{n,K}\right)\right)$ is always surjective. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_16199 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Dual partially harmonic tensors and quantized Schur--Weyl duality Wang, Pei Xiao, Zhankui Quantum Algebra Representation Theory 20C08, 20G15, 20M30 Let $V$ be a $2m$-dimensional symplectic space over an infinite field $K$. Let $\mathfrak{B}^{(f)}_{n,K}$ be the two-sided ideal of the Birman--Murakami--Wenzl algebra $\mathfrak{B}_{n,K}$ generated by $E_1E_3\cdots E_{2f-1}$ with $1\leq f\leq\left\lfloor \frac n2 \right\rfloor$. In this paper, using the diagram category of framed tangles and canonical basis, we prove that the natural homomorphism from $\mathfrak{B}_{n,K}/\mathfrak{B}^{(f)}_{n,K}$ to $ \mathrm{End}_{U_q(\mathfrak{sp}_{2m})}\left(V^{\otimes n}/\left(V^{\otimes n}\cdot \mathfrak{B}^{(f)}_{n,K}\right)\right)$ is always surjective. |
| title | Dual partially harmonic tensors and quantized Schur--Weyl duality |
| topic | Quantum Algebra Representation Theory 20C08, 20G15, 20M30 |
| url | https://arxiv.org/abs/2602.16199 |