Journal Home Page Cumulative Index List of all Volumes Complete Contentsof this Volume Previous Article Journal of Lie Theory 24 (2014), No. 4, 1047--1066Copyright Heldermann Verlag 2014 Branching Laws of Parabolic Verma Modules for Non-symmetric Polar Pairs Haian He Department of Mathematics, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong and: Department of Mathematics, Shanghai Jiao Tong University, 800 Dongchuan Road, Minhang District, Shanghai, P. R. China hebe.hsinchu@yahoo.com.tw [Abstract-pdf] \def\g{{\frak g}} \def\C{{\Bbb C}} We give branching formulas from so$(7,\C)$ to $\g_2$ for parabolic Verma modules attached to $\g_2$-compatible parabolic subalgebras of so$(7,\C)$, and branching formulas from $\g_2$ to sl$(3,\C)$ for parabolic Verma modules attached to sl$(3,\C)$-compatible parabolic subalgebras of $\g_2$ respectively, under some assumptions on the parameters of parabolic Verma modules. Keywords: Branching law, parabolic Verma module, polar pair, Lie algebra. MSC: 17B10 [ Fulltext-pdf (402 KB)] for subscribers only.