Branching Laws of Generalized Verma Modules for Non-symmetric Polar Pairs

Abstract

We give branching formulas from $so(7,\mathbb{C})$ to ${\mathfrak{g}}_2$ for generalized Verma modules attached to ${\mathfrak{g}}_2$-compatible parabolic subalgebras of $so(7,\mathbb{C})$, and branching formulas from ${\mathfrak{g}}_2$ to $sl(3,\mathbb{C})$ for generalized Verma modules attached to $sl(3,\mathbb{C})$-compatible parabolic subalgebras of ${\mathfrak{g}}_2$ respectively, under some assumptions on the parameters of generalized Verma modules.

arXiv comment24 pages, accepted by Journal of Lie Theory