I'm trying to understand how the representation theory of $U_q(\mathfrak{sl}(2))$ works and I had a look to some books and lecture notes available on the internet. The case of $q^m\neq1$ is discussed everywhere, but I'm having a hard time finding reliable (and clear) sources for representation theory for $q$ being a root of unity.

I've understood that when $q$ is a root of unity some of the spin $j\in\frac{1}{2}\mathbb{Z}$ representations become reducible while remaining indecomposable. But how do their tensor product representations behave? I've read on some references the $q$-deformed Clebsch–Gordan coefficients for $q^m\neq1$, but I was unable to find a section dedicated to tensor product representations for $q^m=1$.

Can we still define some sort of Clebsch–Gordan coefficients also when $q^m=1$? I've read something about “removing” representations and defining truncated tensor products, but the statements were confusing… what happens there? I would appreciate some reference suggestions.

I'm trying to understand how the representation theory of $U_q(\mathfrak{sl}(2))$ works and I had a look to some books and lecture notes available on the internet. The case of $q^m\neq1$ is discussed everywhere, but I'm having a hard time finding reliable (and clear) sources for representation theory for $q$ being a root of unity.

I've understood that when $q$ is a root of unity, some of the spin $j\in\frac{1}{2}\mathbb{Z}$ representations become reducible while remaining indecomposable. But how do their tensor product representations behave? I've read in some references about the $q$-deformed Clebsch–Gordan coefficients for $q^m\neq1$, but I was unable to find a section dedicated to tensor product representations for $q^m=1$.

Can we still define some sort of Clebsch–Gordan coefficients also when $q^m=1$? I've read something about “removing” representations and defining truncated tensor products, but the statements were confusing... what happens there? I would appreciate some reference suggestions.

I'm trying to understand how the representation theory of $U_q(sl(2))$ works and I had a look to some books and lecture notes available on the internet. The case of $q^m\neq1$ is discussed everywhere, but I'm having a hard time finding reliable (and clear) sources for representation theory for $q$ being a root of unity.

I've understood that when $q$ is a root of unity some of the spin $j\in\frac{1}{2}\mathbb{Z}$ representations become reducible while remaining indecomposable. But how do their tensor product representations behave? I've read on some references the q-deformed Clebsch-Gordan coefficients for $q^m\neq1$, but I was unable to find a section dedicated to tensor product representations for $q^m=1$.

Can we still define some sort of Clebsch-Gordan coefficients also when $q^m=1$? I've read something about “removing” representations and defining truncated tensor products, but the statements were confusing... what happens there? I would appreciate some reference suggestions. Thank you in advance!

I'm trying to understand how the representation theory of $U_q(\mathfrak{sl}(2))$ works and I had a look to some books and lecture notes available on the internet. The case of $q^m\neq1$ is discussed everywhere, but I'm having a hard time finding reliable (and clear) sources for representation theory for $q$ being a root of unity.

I've understood that when $q$ is a root of unity some of the spin $j\in\frac{1}{2}\mathbb{Z}$ representations become reducible while remaining indecomposable. But how do their tensor product representations behave? I've read on some references the $q$-deformed Clebsch–Gordan coefficients for $q^m\neq1$, but I was unable to find a section dedicated to tensor product representations for $q^m=1$.

Can we still define some sort of Clebsch–Gordan coefficients also when $q^m=1$? I've read something about “removing” representations and defining truncated tensor products, but the statements were confusing… what happens there? I would appreciate some reference suggestions.

I'm trying to understand how the representation theory of $U_q(sl(2))$ works and I had a look to some books and lecture notes available on the internet. The case of $q^m\neq1$ is discussed everywhere, but I'm having a hard time finding reliable (and clear) sources for representation theory for $q$ being a root of unity.

I've understood that when $q$ is a root of unity some of the spin $j\in\frac{1}{2}\mathbb{Z}$ representations become reducible while remaining indecomposable. But how do their tensor product representations behave? I've read on some references the q-deformed Clebsch-Gordan coefficients for $q^m\neq1$, but I was unable to find a section dedicated to tensor product representations for $q^m=1$.

Can we still define some sort of Clebsch-Gordan coefficients also when $q^m=1$? I've read something about “removing” representations and defining truncated tensor products... what happens there? I would appreciate some reference suggestions. Thank you in advance!

I'm trying to understand how the representation theory of $U_q(sl(2))$ works and I had a look to some books and lecture notes available on the internet. The case of $q^m\neq1$ is discussed everywhere, but I'm having a hard time finding reliable (and clear) sources for representation theory for $q$ being a root of unity.

I've understood that when $q$ is a root of unity some of the spin $j\in\frac{1}{2}\mathbb{Z}$ representations become reducible while remaining indecomposable. But how do their tensor product representations behave? I've read on some references the q-deformed Clebsch-Gordan coefficients for $q^m\neq1$, but I was unable to find a section dedicated to tensor product representations for $q^m=1$.

Can we still define some sort of Clebsch-Gordan coefficients also when $q^m=1$? I've read something about “removing” representations and defining truncated tensor products, but the statements were confusing... what happens there? I would appreciate some reference suggestions. Thank you in advance!