论文标题
Quantum Queer Superalgebra不变理论的第一个基本定理
The first fundamental theorem of invariant theory for the quantum queer superalgebra
论文作者
论文摘要
酷儿谎言的经典不变理论是对$ \ m atrm {u}（\ mathfrak {\ mathfrak {q} _n）$ - 对称的超级algebra $ \ \ mathrm {sym}（sym}（sym}（v^^^{ $ v = \ mathbb {c}^{n | n} $。我们建立了量子Queer Superalgebra $ \ Mathrm {u} _Q（\ Mathfrak {q} _n）$不变理论的第一个基本定理。关键成分是一种量子模拟$ \ MATHCAL {o} _ {r，s} $的对称superalgebra $ \ mathrm {sym}（v^{\ oplus r} \ oplus r} \ oplus v^{ $ \ MATHSF {a} _ {r，n} $的$ \ MATHRM {sym}（v^{\ oplus r}）$和量化$ \ bar {\ mathsf {a}} _ {a}} _ {s，s，n} $ $ \ \ mathrm {sym} $ {sym} $ {由于量子Queer Superalgebra $ \ Mathrm {U} _Q（\ Mathfrak {Q} _n）$不是准三角形，因此我们的编织张量产品是通过明确的相互交织的操作员而不是通用$ \ Mathcal {r} $ - r} $ - 矩阵来创建的。
The classical invariant theory for the queer Lie superalgebra is an investigation of the $\mathrm{U}(\mathfrak{q}_n)$-invariant sub-superalgebra of the symmetric superalgebra $\mathrm{Sym}(V^{\oplus r}\oplus V^{*\oplus s})$ for $V=\mathbb{C}^{n|n}$. We establish the first fundamental theorem of invariant theory for the quantum queer superalgebra $\mathrm{U}_q(\mathfrak{q}_n)$. The key ingredient is a quantum analog $\mathcal{O}_{r,s}$ of the symmetric superalgebra $\mathrm{Sym}(V^{\oplus r}\oplus V^{*\oplus s})$ that is created as a braided tensor product of a quantization $\mathsf{A}_{r,n}$ of $\mathrm{Sym}(V^{\oplus r})$ and a quantization $\bar{\mathsf{A}}_{s,n}$ of $\mathrm{Sym}(V^{*\oplus s})$. Since the quantum queer superalgebra $\mathrm{U}_q(\mathfrak{q}_n)$ is not quasi-triangular, our braided tensor product is created via an explicit intertwining operator instead of the universal $\mathcal{R}$-matrix.
