
Journal of Lie Theory 24 (2014), No. 4, 10471066 Copyright Heldermann Verlag 2014 Branching Laws of Parabolic Verma Modules for Nonsymmetric 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 [Abstractpdf] \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 [ Fulltextpdf (402 KB)] for subscribers only. 