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Intermediate lattices $C\mathbb{Z}^n \subseteq \Lambda \subseteq \mathbb{Z}^n$

Let $C \in \mathfrak{gl}(\mathbb{Z},n)$ be a symmetric full rank integer valued matrix (in my case it is the symmetric part of a Cartan matrix). Let $\Lambda \subseteq \mathbb{Z}^n$ be a full rank ...