Modular Valenced Temperley-Lieb Algebras

2021/08/23 by Robert A. Spencer, Spencer, R. A.
Mathematics · #Advanced Combinatorial Mathematics #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2108.10011

openalex publication_date 2021/08/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We investigate the representation theory of the valenced Temperley-Lieb algebras in mixed characteristic. These algebras, as described in characteristic zero by Flores and Peltola, arise naturally in statistical physics and conformal field theory and are a natural deformation of normal Temperley-Lieb algebras. In general characteristic, they encode the fusion rules for the category of U_q(\mathfraksl₂) tilting modules. We use the cellular properties of the Temperley-Lieb algebras to determine those of the valenced Temperley-Lieb algebras. Our approach is, at heart, entirely diagrammatic and we calculate cell indices, module dimensions and indecomposable modules for a wide class of valenced Temperley-Lieb algebras. We present a general framework for finding bases of cell modules and a formula for their dimensions.

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