论文标题
Temperley-Lieb，Birman-Murakami-Wenzl和Askey-Wilson代数以及其他$ U_Q（\ Mathfrak {SL} _2）$
Temperley-Lieb, Birman-Murakami-Wenzl and Askey-Wilson algebras and other centralizers of $U_q(\mathfrak{sl}_2)$
论文作者
论文摘要
$ u_q（\ mathfrak {sl} _2）$在三种不可约表示的张量产物中的对角线嵌入图像的中心化。目的是提供有关发电机和关系的描述。在这方面提供了一个猜想，以作为Askey-Wilson代数的商的中心化来提供。对猜想的支持是通过检查商的表示形式提供的。在许多情况下，猜想也被证明是正确的，因此特别表现出temberley-lieb，birman-murakami-wenzl和一边界temberley-lieb代数作为Askey-Wilson代数的商。
The centralizer of the image of the diagonal embedding of $U_q(\mathfrak{sl}_2)$ in the tensor product of three irreducible representations is examined in a Schur-Weyl duality spirit. The aim is to offer a description in terms of generators and relations. A conjecture in this respect is offered with the centralizers presented as quotients of the Askey-Wilson algebra. Support for the conjecture is provided by an examination of the representations of the quotients. The conjecture is also shown to be true in a number of cases thereby exhibiting in particular the Temperley-Lieb, Birman-Murakami-Wenzl and one-boundary Temperley-Lieb algebras as quotients of the Askey-Wilson algebra.
