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arXiv · 1209.3970

The branching problem for generalized Verma modules, with application to the pair $(so(7),Lie G_2)$, extended version with tables

Todor Milev·Petr Somberg
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Abstract

We discuss the branching problem for generalized Verma modules $M_\lambda(\mathfrak g, \mathfrak p)$ applied to couples of reductive Lie algebras $\bar{\mathfrak g}\hookrightarrow \mathfrak g$. The analysis is based on projecting character formulas to quantify the branching, and on the action of the center of $U(\bar{\mathfrak g})$ to explicitly construct singular vectors realizing part of the branching. We demonstrate the results on the pair $\mathrm{Lie}G_2\hookrightarrow{so(7)}$ for both strongly and weakly compatible with $i(\mathrm {Lie} G_2)$ parabolic subalgebras and a large class of inducing representations.

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Todor Milev, Petr Somberg. 2012-09-18. The branching problem for generalized Verma modules, with application to the pair $(so(7),Lie G_2)$, extended version with tables. https://arxiv.org/abs/1209.3970

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