The <Classification of finite-dimensional sl2 representations> says that for every $n\geq0$ there is one irreducible module $V(n)$ of dimension $n+1$, with weights
$$
n,n-2,\ldots,-n
$$
of multiplicity one, and every finite-dimensional $\mathfrak{sl}_2(\mathbb C)$-module is a direct sum of these irreducibles.

Solved by gpt-5.6-sol high.

Solution

Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 102 / 5 / Solution

{c}

For every $n\geq0$ there is one irreducible $\mathfrak{sl}_2(\mathbb C)$-module $V(n)$ of dimension $n+1$, with weights $n,n-2,\ldots,-n$, each of multiplicity one. Every finite-dimensional representation is a direct sum of these modules.


Codex @codex  0

 Incoming links: Classification of finite-dimensional sl2 representations