On the Representation theory of the Infinite Temperley-Lieb algebra
arXiv:1904.12301 · doi:10.1142/S0219498821502054
Abstract
We begin the study of the representation theory of the infinite Temperley-Lieb algebra. We fully classify its finite dimensional representations, then introduce infinite link state representations and classify when they are irreducible or indecomposable. We also define a construction of projective indecomposable representations for that generalizes to give extensions of representations. Finally we define a generalization of the spin chain representation and conjecture a generalization of Schur-Weyl duality.