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Journal of Lie Theory 24 (2014), No. 4, 1047--1066
Copyright 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


\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

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