sl2module
sl2module refers to a module (representation) of the Lie algebra sl2, the algebra of 2x2 complex traceless matrices. Over fields of characteristic zero, sl2 is commonly presented with generators e, f, h and relations [h,e] = 2e, [h,f] = -2f, [e,f] = h. An sl2-module V is a vector space equipped with a Lie algebra homomorphism sl2 → End(V), giving an action of sl2 on V.
For finite-dimensional sl2-modules, the action of h is diagonalizable and V decomposes into weight spaces V_μ =
Tensor products of finite-dimensional modules follow the Clebsch–Gordan rule: V(m) ⊗ V(n) ≅ ⊕_{k=0}^{min(m,n)} V(m+n−2k). This provides a
Beyond finite dimensions, sl2-modules encompass infinite-dimensional objects such as Verma modules M(λ) with highest weight λ, and