References & Citations
Mathematics > Representation Theory
Title: Projection of root systems
(Submitted on 3 Apr 2019 (v1), last revised 6 May 2024 (this version, v3))
Abstract: Let $a$ be a real euclidean vector space of finite dimension and $\Sigma$ a root system in $a$ with a basis $\Delta$. Let $\Theta \subset \Delta$ and $M = M_{\Theta}$ be a standard Levi of a reductive group $G$ such that $a_\Theta = a_M / a_G$. Let us denote $d$ the dimension of $a_\Theta$, i.e the cardinal of $\Delta - \Theta$ and $\Sigma_{\Theta}$ the set of all non-trivial projections of roots in $\Sigma$. We obtain conditions on $\Theta$ such that $\Sigma_\Theta$ contains a root system of rank $d$.
Submission history
From: Sarah Dijols [view email][v1] Wed, 3 Apr 2019 09:54:12 GMT (26kb)
[v2] Tue, 27 Aug 2019 03:21:24 GMT (26kb)
[v3] Mon, 6 May 2024 22:47:31 GMT (0kb,I)
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