Composition of Kinetic Momenta: The U_q(sl(2)) case

TL;DR

This paper investigates how tensor products of finite-dimensional irreducible representations of the quantum group U_q(sl(2)) decompose at roots of unity, revealing the structure of irreducible and indecomposable components.

Contribution

It provides a detailed decomposition of tensor products of U_q(sl(2)) representations at roots of unity, including both restricted and unrestricted cases.

Findings

Decomposition into irreducible and indecomposable representations.

Explicit structure of tensor products at roots of unity.

Extension of representation theory for quantum groups.

Abstract

The tensor products of (restricted and unrestricted) finite dimensional irreducible representations of $\uq$ are considered for $q$ a root of unity. They are decomposed into direct sums of irreducible and/or indecomposable representations.