2019/09/04 by Zhuohui Zhang, Zhang, Zhuohui
Mathematics · Physics and Astronomy · #11F55 #11F70 (primary) #33C47 #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Number Theory (math.NT) #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.1909.01510
openalex publication_date 2019/09/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We calculate the (\mathfrakg,K) module structure for the principal series representation of Sp(4,ℝ). Furthermore, we introduced a hypergeometric generating function together with an inverse Mellin transform technique as an improvement to the method to calculate the intertwining operators. We have shown that the matrix entries of the simple intertwining operators for Sp(4,ℝ)-principal series are Hahn polynomials, and the matrix entries of the long intertwining operator can be expressed as the constant term of the Laurent expansion of some hypergeometric function.