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dc.contributor.advisorCornwell, J. F.en
dc.contributor.authorAssar, Ali Rezaen
dc.description.abstractLet G be a locally compact group and G'CG a subgroup. Suppose that we are given an irreducible unitary representation Γ of G (which is infinite dimensional and is specified by the so-called principal series representation) and we wish to find out how this representation reduces on the subgroup G'. In the special case where the representation Γ of G is an induced representation, then one can first apply Mackey's subgroup theorem. This gives a representation Γ’of G* defined on a Hilbert space 𝓗. However it often happens that Γ is not an irreducible representation of G , nor even a direct sum of irreducible representations, but is a "direct integral" of irreducible representations. In this work, a unitary transformation will be introduced that maps 𝓗’ into another Hilbert space 𝓗’^ which is a direct integral of the Hilbert spaces of the irreducible representation that appear in the reduction of the principal series representation Γ on G’. The group G under consideration is taken to be SL(2,C) which is the universal covering of Lorentz Group , 1 B and G an Abelian subgroup (1,0 β 1)which is called the horospherical subgroup of SL(2,C) and we seek the reduction as mentioned above.en
dc.publisherUniversity of St Andrewsen
dc.subject.lcshAbelian groupsen
dc.subject.lcshLorentz groupsen
dc.subject.lcshGroup theoryen
dc.titleReduction of the principal series representation of Lorentz groups on an Abelian subgroupen
dc.type.qualificationnameMSc Master of Scienceen
dc.publisher.institutionThe University of St Andrewsen

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