AI 中文总结
本文针对𝔰𝔬ₘ⊂𝔰𝔩ₘ对称对，利用(Oₘ,𝔰𝔬₂ₙ)自旋Howe对偶，证明了边界Casimir联络单值化与ι量子Weyl群的辫群有限维线性表示同构，建立了对应Kohno–Drinfeld定理。
AI 中文摘要
我们证明了辫群的两个有限维线性表示是同构的：一个来自边界Casimir联络的单值化，另一个来自ι量子Weyl群，二者对任意分裂对称对𝔨⊂𝔤及𝔨的任意可积表示均有定义。我们的证明利用了(Oₘ,𝔰𝔬₂ₙ)自旋Howe对偶，因此仅适用于𝔰𝔬ₘ⊂𝔰𝔩ₘ这一对。
英文摘要
We prove that two finite-dimensional linear representations of the braid group are isomorphic. One representation comes from the monodromy of the boundary Casimir connection, and the other comes from the $ι$quantum Weyl group. Both representations are defined for any split symmetric pair $\mathfrak{k}\subset \mathfrak{g}$ and for any integrable representation of $\mathfrak{k}$. Our proof uses $(O_m,\mathfrak{so}_{2n})$ spin Howe duality, so it is only for the pair $\mathfrak{so}_m\subset \mathfrak{sl}_m$.
Comments31 pages, comments welcome!
