## The representation theory of seam algebras

Alexis Langlois-Rémillard, Yvan Saint-Aubin

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

- doi: 10.21468/SciPostPhys.8.2.019
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### Abstract

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.

### Ontology / Topics

See full Ontology or Topics database.### Authors / Affiliations: mappings to Contributors and Organizations

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^{1 }Alexis Langlois-Rémillard, -
^{2 }Yvan Saint-Aubin

- Fonds Québécois de la Recherche sur la Nature et les Technologies (through Organization: Fonds de Recherche du Québec – Nature et technologies [FRQNT])
- Fonds Wetenschappelijk Onderzoek (FWO) (through Organization: Fonds voor Wetenschappelijk Onderzoek - Vlaanderen / Research Foundation - Flanders [FWO])
- Conseil National de Recherches Canada / National Research Council Canada [CNRC]