TY - JOUR TI - Decomposition of principal series representations and Clebsch-Gordan coefficients DO - https://doi.org/doi:10.7282/t3-sv7e-jz28 PY - 2018 AB - In this thesis, following a similar procedure developed by Buttcane and Miller in "Weights, raising and lowering operators, and K-types for automorphic forms on SL(3,R)" for SL(3,R), the (g,K)-module structures of the minimal principal series of real reductive Lie groups SU(2,1) and Sp(4,R) are described explicitly by realizing the representations in the space of K-finite functions on U(2). Moreover, by combining combinatorial techniques and contour integrations, this thesis introduces a method of calculating intertwining operators on the principal series. Upon restriction to each K-type, the matrix entries of intertwining operators are represented by Gamma-functions and Laurent series coefficients of hypergeometric series. The calculation of the (g,K)-module structure of principal series can be generalized to real reductive Lie groups whose maximal compact subgroup is a product of SU(2)'s and U(1)'s. KW - Mathematics KW - Lie groups LA - eng ER -