论文标题
类型$ \ mathbf {bd} $ a二元二元性通过$ q $ -clifford代数
Skew Howe duality for Types $\mathbf{BD}$ via $q$-Clifford algebras
论文作者
论文摘要
我们通过SEESAW将$ \ mathbf {a} $代数类型的量化偏差二元性结果扩展到正交类型。我们使用量化的Clifford代数中的双中心属性，开发了$ u_q（\ mathfrak {so} _n）$的第一个不变理论基本理论基本定理的运算符。我们通过明确计算$ u_q（\ mathfrak {so} so} _ {2n} _ {2n}）\ otime u_q'的$ u_q（\ mathfrak {so} _ {2n}）$ spin表示的张量的无多性分解。 Clifford代数是我们工作的重要特征：它们为经典和量化的偏差二元性结果提供了一个统一的框架，可以扩展到包括类型的$ \ Mathbf {bd} $的正交代数。
We extend a quantized skew Howe duality result for Type $\mathbf{A}$ algebras to orthogonal types via a seesaw. We develop an operator commutant version of the First Fundamental Theorem of invariant theory for $U_q(\mathfrak{so}_n)$ using a double centralizer property inside a quantized Clifford algebra. We obtain a multiplicity-free decomposition of tensor powers of the $U_q(\mathfrak{so}_{2n})$ spin representation by explicitly computing joint highest weights with respect to an action of $U_q(\mathfrak{so}_{2n}) \otimes U_q'(\mathfrak{so}_m)$. Clifford algebras are an essential feature of our work: they provide a unifying framework for classical and quantized skew Howe duality results that can be extended to include orthogonal algebras of types $\mathbf{BD}$.
