Decompositions of tensor products of infinite and finite dimensional representations of semisimple groups
Let G be a connected semisimple Lie group with finite centre, A a Harish- Chandra G-module, F a finite-dimensional simple G-module. In the first part decomposition formulas are derived for the Harish-Chandra character of \(F\otimes A\) on a Cartan subgroup if A belongs to the principal series or to the discrete series. In the second part these formulas are used for the case that G is a Lorentz group and A is simple to obtain the decomposition of the character of \(F\otimes A\) into irreducible characters, by means of T. Hirai's description of the irreducible characters of the Lorentz groups.
scientific article; zbMATH DE number 3916602