On the structure of the blob algebra
The aim of this paper is to understand the structure of the standard modules for the two-parameter blob algebra, \(b_n(q,q')\), an algebra arising from the context of transfer matrix algebras in statistical mechanics. Working over a field of characteristic zero, the authors are able to determine the structure of the standard modules for the algebra quite explicitly, obtaining precise results on homomorphisms between standard modules, the blocks of the algebra and the filtration into simple modules of various standard modules. The techniques used involve homological algebra and the calculus of diagrams for \(b_n(q,q')\). The results provide further evidence for a connection with category \(\mathcal O\) for \(\widehat{sl}_2\).
scientific article; zbMATH DE number 1429479