The representation theory of seam algebras

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 Crampé and Poulain d'Andecy.

arXiv comment30 pages, 4 figures, typos corrected, improved history of seam algebras

References in corpus (7)

• Logarithmic Minimal Models
• The Blob Algebra and the Periodic Temperley-Lieb Algebra
• Conformal boundary loop models
• Boundary algebras and Kac modules for logarithmic minimal models
• Combinatorial aspects of boundary loop models
• Cellularity of Wreath Product Algebras and $A$--Brauer algebras
• The principal indecomposable modules of the dilute Temperley-Lieb algebra

Cited by in corpus (3)

• Baxterisation of the fused Hecke algebra and R-matrices with gl(N)-symmetry
• Fused Hecke algebra and one-boundary algebras
• Uncoiled affine Temperley-Lieb algebras and their Wenzl-Jones projectors