Diagrammatic representations of Generalized Temperley-Lieb algebras of affine type \widetildeB and \widetildeD

2022/12/22 by Riccardo Biagioli, Biagioli, Riccardo, Giuliana Fatabbi +3
Mathematics · #05E10 #16G30 #Advanced Combinatorial Mathematics #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2212.11588

openalex publication_date 2022/12/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let (W,S) be an affine Coxeter system of type \widetildeB or \widetildeD and \rm TL(W) the corresponding generalized Temperley-Lieb algebra. In this paper we define an infinite dimensional associative algebra made of decorated diagrams that is isomorphic to \rm TL(W). Moreover, we describe an explicit basis for such an algebra consisting of special decorated diagrams that we call admissible. Such basis is in bijective correspondence with the classical monomial basis of the generalized Temperley-Lieb algebra indexed by the fully commutative elements of W.

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