论文标题
部分temperley-lieb代数及其表示形式
The partial Temperley-Lieb algebra and its representations
论文作者
论文摘要
我们给出一个新图代数的组合描述，部分templey- lieb代数，作为通用的中央式代数$ \ mathrm {end} _ {\ mathbf {u} _q（u} _q（\ mathfrak {\ mathfrak {gl} _2） v（1）$是量化包络代数$ \ mathbf {u} _q（\ mathfrak {gl} _2）$的量化和天然模块的直接总和。这是Benkart和Halverson的Motzkin代数（$ \ Mathbf {u} _Q（\ Mathfrak {sl} _2）$ - centralizer）的适当子代数。我们证明了Schur的版本 - 新代数的二元性，并描述了他们的通用表示理论。
We give a combinatorial description of a new diagram algebra, the partial Temperley--Lieb algebra, arising as the generic centralizer algebra $\mathrm{End}_{\mathbf{U}_q(\mathfrak{gl}_2)}(V^{\otimes k})$, where $V = V(0) \oplus V(1)$ is the direct sum of the trivial and natural module for the quantized enveloping algebra $\mathbf{U}_q(\mathfrak{gl}_2)$. It is a proper subalgebra of the Motzkin algebra (the $\mathbf{U}_q(\mathfrak{sl}_2)$-centralizer) of Benkart and Halverson. We prove a version of Schur--Weyl duality for the new algebras, and describe their generic representation theory.
