This paper gives an introduction to Temperley-Lieb algebra that is easily accessible to undergraduates, presenting TL diagrams, the method for multiplying the diagrams, and the properties of the multiplication that it is necessary to preserve in a representation. The paper also gives a method for finding representations of the TL monoids (sets of diagrams classified by number of vertices) using Young tableaux, and shows that these representations are all of the irreducible representations. While ideas of Hecke algebra imply the fact that this method produces representations, this paper provides a direct proof, strictly within the field of representation theory. It also introduces some conclusions about the rank of a diagram and its action on the tableaux.
Moore, Anne, "Representations of the Temperley-Lieb Algebra" (2008). Mathematics, Statistics, and Computer Science Honors Projects. 11.
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