量子对角代数与伪格代数
Quantum Diagonal Algebra and Pseudo-Plactic Algebra
摘要：
量子矩阵群的对角元的子代数被Daniel Krob和Jean-Yves Thibon证明为同构于一个三次代数，称为量子伪代数。我们利用量子群与Hecke代数之间的量子Schur-Weyl对偶性，给出了一个证明该猜想的函子方法.通过一个适当的Schur函子，发现量子对角子代数的关系是底层Hecke代数的辫子关系的象，从而给出了猜想的一个直接证明.
英文摘要：
The subalgebra of diagonal elements of a quantum matrix group has been conjectured by Daniel Krob and Jean-Yves Thibon to be isomorphic to a cubic algebra, coined the quantum pseudo-plactic algebra. We present a functorial approach to the conjecture through the quantum Schur-Weyl duality between the quantum group and the Hecke algebra. The relations of the quantum diagonal subalgebra are found to be the image of the braid relations of the underlying Hecke algebra by an appropriate Schur functor which gives a straightforward proof of the conjecture.
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