The representation theory of seam algebras

The boundary seam algebras \mathsf{b}_{n,k}(\beta=q+q^{-1}) 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}(\beta=q+q^{-1}) 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 Crampe and Poulain d’Andecy.