论文标题
单一豪双对的变形
Deformations of unitary Howe dual pairs
论文作者
论文摘要
我们研究Howe Dual对$（\ Mathrm {u}（n），\ Mathfrak {u}（1,1）））$和$（\ Mathrm {u}（n），\ Mathfrak {u}（u}（2 | 1））$与Rational cherednik e ggebra a $ h_ y y a的上下文组$ g $在实际矢量空间$ e $ e $均匀的尺寸上作用。对于每一对，我们表明一个伙伴的谎言（超级）代数结构保留在变形下，这会导致标准模块或其带有旋转空间的标准模块的多重分解。对于$ e $是二维而$ g $的情况，我们为变形对和相关的联合分解提供了完整的描述。
We study deformations of the Howe dual pairs $(\mathrm{U}(n),\mathfrak{u}(1,1))$ and $(\mathrm{U}(n),\mathfrak{u}(2|1))$ to the context of a rational Cherednik algebra $H_{1,c}(G,E)$ associated with a real reflection group $G$ acting on a real vector space $E$ of even dimension. For each pair, we show that the Lie (super)algebra structure of one partner is preserved under the deformation, which leads to a multiplicity-free decomposition of the standard module or its tensor product with a spinor space. For the case where $E$ is two-dimensional and $G$ is a dihedral group, we provide complete descriptions for the deformed pair and the relevant joint-decomposition.
