The Temperley Lieb algebra $TL_n$ at roots of unity is not semisimple. The standard representations $V_{n,p}$ are indecomposable but, in general, not irreducible. If $K_{n,p}$ is the sub-representation of $V_{n,p}$ given by the kernel of the usual bilinear form, the quotients $V_{n,p}/K_{n,p}$ are irreducible. For one dimensional representations, we have the trivial representation, and additionally, we sometimes have certain special one dimensional representations at roots of unity - for example at $\delta = 1$ ($q = \zeta_{12}$), we have two additional one dimensional representations - If we let $u_1,..,u_{n-1}$ be the generators of $TL_n$, we could send every $u_i$ to either $+1$ or $-1$, and this would define a representation. My question is: are there any others? Could there by some other indecomposable representation which is not listed above?
Thank you in advance.
