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Diagram calculus for a type affine \(C\) Temperley-Lieb algebra. II. (English) Zbl 06902465
Summary: In a previous paper, we presented an infinite dimensional associative diagram algebra that satisfies the relations of the generalized Temperley-Lieb algebra having a basis indexed by the fully commutative elements of the Coxeter group of type affine \(C\). We also provided an explicit description of a basis for the diagram algebra. In this paper, we show that the diagrammatic representation is faithful and establish a correspondence between the basis diagrams and the so-called monomial basis of the Temperley-Lieb algebra of type affine \(C\).

MSC:
20F55 Reflection and Coxeter groups (group-theoretic aspects)
20C08 Hecke algebras and their representations
57M15 Relations of low-dimensional topology with graph theory
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