The representation theory of seam algebras

The boundary seam algebras were introduced by Morin-Duchesne, Ridout and Rasmussen to formulatealgebraically a large class of boundary conditions for two-dimensionalstatistical loop models. The representation theory of these algebras is given: their irreducible, standard (cellular) and principal modules are constructed and their structure explicited in terms of theircomposition factors and of non-split short exact sequences. Thedimensions of the irreducible modules and of the radicals of standardones are also given. The methods proposed here might be applicable to alarge family of algebras, for example to those introduced recently byFlores and Peltola, and Crampé and Poulain d’Andecy.The boundary seam algebras were introduced by Morin-Duchesne, Ridout and Rasmussen to formulatealgebraically a large class of boundary conditions for two-dimensionalstatistical loop models. The representation theory of these algebras is given: their irreducible, standard (cellular) and principal modules are constructed and their structure explicited in terms of theircomposition factors and of non-split short exact sequences. Thedimensions of the irreducible modules and of the radicals of standardones are also given. The methods proposed here might be applicable to alarge family of algebras, for example to those introduced recently byFlores and Peltola, and Crampé and Poulain d’Andecy.A