SciPost logo

The representation theory of seam algebras

Alexis Langlois-Rémillard, Yvan Saint-Aubin

SciPost Phys. 8, 019 (2020) · published 5 February 2020


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

Cited by 3

Crossref Cited-by

Ontology / Topics

See full Ontology or Topics database.

Loop models

Authors / Affiliations: mappings to Contributors and Organizations

See all Organizations.
Funders for the research work leading to this publication