Restriction and induction of indecomposable modules over the Temperley-Lieb algebras

Understand

Both the original Temperley-Lieb algebras $\mathsf{TL}_{n}$ and their dilute counterparts $\mathsf{dTL}_{n}$ form families of filtered algebras: $\mathsf{TL}_{n}\subset \mathsf{TL}_{n+1}$ and $\mathsf{dTL}_{n}\subset\mathsf{dTL}_{n+1}$, for all $n\geq 0$.

• For each such inclusion, the restriction and induction of every finite-dimensional indecomposable module over $\mathsf{TL}_{n}$ (or $\mathsf{dTL}_{n}$) is computed.
• To accomplish this, a thorough description of each indecomposable is given, including its projective cover and injective hull, some short exact sequences in which it appears, its socle and head, and its extension groups with irreducible modules.
• These data are also used to prove the completeness of the list of indecomposable modules, up to isomorphism.