The representation theory of seam algebras
Article [Author's Original]
Abstract(s)
The boundary seam algebras \(b_{n,k} (\beta = q + q^{-1})\) 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 \(b_{n,k} (\beta = q + q^{-1})\) 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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