论文标题
$ g（R，P，N）$的广义templeley-lieb代数
Generalised Temperley-Lieb algebras of type $G(r,p,n)$
论文作者
论文摘要
在较早的工作中，我们定义了``广泛的temperley-lieb代数''$ tl_ {r，1，n} $，与不良反射组$ g（r，1，n）$相对应为Cyclotomic Hecke algebra的商。在这项工作中，我们介绍了广泛的templeley-lieb代数$ tl_ {r，p，n} $，该$对应于复杂的反射组$ g（r，p，p，n）$。我们的定义将$ tl_ {r，p，n} $确定为$ tl_ {r，1，n} $的定点子级，在某个自动形态$σ$下。我们证明$σ$相对于$ tl_ {r，1，n} $的蜂窝结构，证明了$ tl_ {r，p，n} $的细胞性。我们还对$ tl_ {r，p，n} $的细胞模块及其分解数字进行了描述，最后我们指出了我们的代数如何被分类并可能导致图表理论。
In an earlier work, we defined a ``generalised Temperley-Lieb algebra'' $TL_{r,1,n}$ corresponding to the imprimitive reflection group $G(r,1,n)$ as a quotient of the cyclotomic Hecke algebra. In this work we introduce the generalised Temperley-Lieb algebra $TL_{r,p,n}$ which corresponds to the complex reflection group $G(r,p,n)$. Our definition identifies $TL_{r,p,n}$ as the fixed-point subalgebra of $TL_{r,1,n}$ under a certain automorphism $σ$. We prove the cellularity of $TL_{r,p,n}$ by proving that $σ$ induces a special shift automorphism with respect to the cellular structure of $TL_{r,1,n}$. We also give a description of the cell modules of $TL_{r,p,n}$ and their decomposition numbers, and finally we point to how our algebras might be categorified and could lead to a diagrammatic theory.
