The Classical Groups. Spectral Analysis of Their Finite-Dimensional Representations

CONTENTSIntroductionPart I. Description of the irreducible representations § 1. Elements of the general theory § 2. The Gauss decomposition § 3. The Lorentz group and the group of rotations of three-dimensional euclidean space § 4. The full linear group § 5. Differential operators on the group Z § 6. The space of irreducible representations § 7. The symplectic group § 8. The orthogonal group § 9. Binary decompositions; symmetric powers of spinor representationsPart II. Some problems of spectral analysis § 10. The product of two irreducible representations of the Lorentz group § 11. Decompositions of tensor representations § 12. Symmetric powers § 13. Reduction of dimension (restriction of representations from a group to a subgroup) § 14. Computation of the spectrum of a tensor product of two irreducible representations § 15. Concrete formulae of spectral analysisReferences