So it is well known that when you tensor together two induced modules for an algebraic group $\nabla(\lambda) \otimes \nabla(\mu)$ that the result has a filtration by other induced modules, (I.e. it has a good filtration.). It is also well known that the sections can be determined by the character formula, $$ \mathrm{ch}(\nabla(\lambda) \otimes \nabla(\mu)) = \sum_{ \nu \mbox{ a weight of }\nabla(\mu)} \chi( \lambda + \nu) $$ where $\chi(\lambda)$ is the (formal) character of $\nabla(\lambda)$.

Can anyone give me a reference for this and/or a name for this character formula? I've seen it variously called "Brauer's character formula" or the "Littlewood-Richardson Rule" which is correct? (I can't seem to find it in Jantzen, I haven't tried anywhere else yet.)

Thanks for your help.