论文标题
模块化temperley-lieb代数
The Modular Temperley-Lieb Algebra
论文作者
论文摘要
我们研究了temperley-lieb代数的表示理论，即$ tl_n（δ）$，该理论定义为在积极特征的领域。我们寻求回答的主要问题是，在任意戒指上$ tl_n $中的单元模块中的简单模块多样性。这为我们提供了该代数的分解编号以及所有简单模块的尺寸。我们从图解原理获得了这些结果，而无需吸引$ tl_n $作为$ u_q（\ Mathfrak {sl} _2）$模块的内态代数的实现。我们的结果严格概括了temperley-lieb代数的已知特征零理论。
We investigate the representation theory of the Temperley-Lieb algebra, $TL_n(δ)$, defined over a field of positive characteristic. The principle question we seek to answer is the multiplicity of simple modules in cell modules for $TL_n$ over arbitrary rings. This provides us with the decomposition numbers for this algebra, as well as the dimensions of all simple modules. We obtain these results from diagrammatic principles, without appealing to realisations of $TL_n$ as endomorphism algebras of $U_q(\mathfrak{sl}_2)$ modules. Our results strictly generalise the known characteristic zero theory of the Temperley-Lieb algebras.
