论文标题
量子组的Capelli特征值问题
The Capelli eigenvalue problem for quantum groups
论文作者
论文摘要
我们介绍并研究了与三个对称对家族相关的新建量子Weyl代数内的量子capelli操作员。特定量化的包围代数的中心和Capelli操作员都在这些量子Weyl代数的多项式部分上进行了半膜。我们展示了如何转移由量子对称对理论引起的中心的众所周知的特性，向Capelli操作员。使用这些信息，我们提供了诺波 - 萨希插值多项式的自然实现，作为产生量子capelli操作员特征值的函数。
We introduce and study quantum Capelli operators inside newly constructed quantum Weyl algebras associated to three families of symmetric pairs. Both the center of a particular quantized enveloping algebra and the Capelli operators act semisimply on the polynomial part of these quantum Weyl algebras. We show how to transfer well-known properties of the center arising from the theory of quantum symmetric pairs to the Capelli operators. Using this information, we provide a natural realization of Knop-Sahi interpolation polynomials as functions that produce eigenvalues for quantum Capelli operators.
