Seam代数的表示理论
The representation theory of seam algebras
摘要：
边界缝代数$\mathsf{b}_{n,k}(β=q+q^{-1})$是由Morin-Duchesne，Ridout和Rasmussen提出的，用于用代数方法表示二维统计环模型的一大类边界条件。给出了这些代数的表示理论$\mathsf{b}_{n,k}(β=q+q^{-1})$：构造了它们的不可约模、标准模（胞腔模）和主模，并根据它们的组成因子和非分裂短正合序列来说明它们的结构。给出了不可约模的维数和标准模的根的维数。这里提出的方法可能适用于一个大家庭的代数，例如最近推出的弗洛雷斯和Peltola，和Crampé和普兰德Andecy。
英文摘要：
The boundary seam algebras $\mathsf{b}_{n,k}(β=q+q^{-1})$ were introduced by Morin-Duchesne, Ridout and Rasmussen to formulate algebraically a large class of boundary conditions for two-dimensional statistical loop models. The representation theory of these algebras $\mathsf{b}_{n,k}(β=q+q^{-1})$ is given: their irreducible, standard (cellular) and principal modules are constructed and their structure explicited in terms of their composition factors and of non-split short exact sequences. The dimensions of the irreducible modules and of the radicals of standard ones are also given. The methods proposed here might be applicable to a large family of algebras, for example to those introduced recently by Flores and Peltola, and Crampé and Poulain d'Andecy.
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