Publikace na Matematicko-fyzikální fakulta |
2014
Abstrakt
We consider the branching problem for generalized Verma modules $M_\lambda(\mathfrak g, \mathfrak p)$ applied to couples of reductive Lie algebras $\bar{\mathfrak g}\stackrel{i}{\hookrightarrow} \mathfrak g$. Our analysis of the problem is based on projecting character formulas to quantify the branching, and on the action of the center of $U(\bar{\mathfrak g})$ to construct explicitly singular vectors realizing the $\bar{\gog}$-top level of the branching.
We compute explicitly the top part of the branching for the pair $\mathrm{Lie~}G_2\stackrel{i} \hookrightarrow{so(7)}$ for both strongly and weakly compatible with $i(\mathrm {Lie~} G_2)$ parabolic subalgebras and a large class of inducing representations.