论文标题
Schur-Weyl二元性，Verma模块和Ariki-Koike代数的行商
Schur-Weyl duality, Verma modules, and row quotients of Ariki-Koike algebras
论文作者
论文摘要
我们证明了$ \ mathfrak {gl} _m $的量子包膜代数与Ariki-koike代数的某些代数，我们明确给出了schur-weyl双重性。二元性涉及多个代数独立的参数，并通过抛物线释放通用Verma模块的张量产物和$ \ Mathfrak {Gl} _M $的自然表示的张量。我们还通过发电机和伍德考克（Martin and Woodcock）的广义代数代数的关系进行了新的演讲，以及通过证明它们作为我们代数的特定情况，对Schur-Weyl二元性的解释进行了解释。
We prove a Schur-Weyl duality between the quantum enveloping algebra of $\mathfrak{gl}_m$ and certain quotient algebras of Ariki-Koike algebras, which we give explicitly. The duality involves several algebraically independent parameters and is realized through the tensor product of a parabolic universal Verma module and a tensor power of the natural representation of $\mathfrak{gl}_m$. We also give a new presentation by generators and relations of the generalized blob algebras of Martin and Woodcock as well as an interpretation in terms of Schur-Weyl duality by showing they occur as a particular case of our algebras.
